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Data Presentation ( CIE A Level Maths: Probability & Statistics 1 )

Revision note.

Data Presentation

What graphs and diagrams should i be familiar with.

•  Can be used with ungrouped data of a single variable
• Shows all the data and the shape of its distribution
• Can be used with ungrouped data of a single variable
• Shows the range, interquartile range and quartiles clearly
• Very useful for comparing data patterns quickly
• Can be used with continuous grouped data of a single variable
• Shows the running total of the frequencies that fall below the upper bound of each class
• Can be used with varying group sizes
• Shows the frequencies of the group, represented by the area of each bar
• You might be expected to draw a full diagram or to add to an incomplete diagram

What should I look out for when interpreting graphs?

• Look carefully at the context of the information given in the graph
• Sometimes the numbers will be abbreviated to fit on the scale, for example if a population is given in millions then the number 60 will represent 60 000 000
• Look carefully at the labels and units to determine how a value should be read
• If there is more than one graph represented on the same set of axes take extra care to ensure you are reading from the correct one
• Beware of misleading graphs, the scales on the axes, units and representation can be manipulated to make a graph look more/less convincing

Worked example

A student is collecting information on his friends’ interests and believes that his friends who only have dogs spend more time outside than his friends who only have cats. He has surveyed 20 friends with only cats and 20 friends with only dogs and has written down the total amount of time, rounded to the nearest hour, each of them spent outside last week. Describe, with a reason, which diagram would be best for the student to use to display the data. 

• Take the time needed when working with diagrams, they are usually ‘easy marks’ questions but it is common for students to rush them and make silly mistakes.

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Author: Dan

Dan graduated from the University of Oxford with a First class degree in mathematics. As well as teaching maths for over 8 years, Dan has marked a range of exams for Edexcel, tutored students and taught A Level Accounting. Dan has a keen interest in statistics and probability and their real-life applications.

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Category Archives: Representation of Data

As-level mathematics (9709) – probability & statistics 1 – representation of data.

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What are the different ways of Data Representation?

The process of collecting the data and analyzing that data in large quantity is known as statistics. It is a branch of mathematics trading with the collection, analysis, interpretation, and presentation of numeral facts and figures.

It is a numerical statement that helps us to collect and analyze the data in large quantity the statistics are based on two of its concepts:

• Statistical Data 
• Statistical Science

Statistics must be expressed numerically and should be collected systematically.

Data Representation

The word data refers to constituting people, things, events, ideas. It can be a title, an integer, or anycast.  After collecting data the investigator has to condense them in tabular form to study their salient features. Such an arrangement is known as the presentation of data.

It refers to the process of condensing the collected data in a tabular form or graphically. This arrangement of data is known as Data Representation.

The row can be placed in different orders like it can be presented in ascending orders, descending order, or can be presented in alphabetical order. 

Example: Let the marks obtained by 10 students of class V in a class test, out of 50 according to their roll numbers, be: 39, 44, 49, 40, 22, 10, 45, 38, 15, 50 The data in the given form is known as raw data. The above given data can be placed in the serial order as shown below: Roll No. Marks 1 39 2 44 3 49 4 40 5 22 6 10 7 45 8 38 9 14 10 50 Now, if you want to analyse the standard of achievement of the students. If you arrange them in ascending or descending order, it will give you a better picture. Ascending order: 10, 15, 22, 38, 39, 40, 44. 45, 49, 50 Descending order: 50, 49, 45, 44, 40, 39, 38, 22, 15, 10 When the row is placed in ascending or descending order is known as arrayed data.

Types of Graphical Data Representation

Bar chart helps us to represent the collected data visually. The collected data can be visualized horizontally or vertically in a bar chart like amounts and frequency. It can be grouped or single. It helps us in comparing different items. By looking at all the bars, it is easy to say which types in a group of data influence the other.

Now let us understand bar chart by taking this example  Let the marks obtained by 5 students of class V in a class test, out of 10 according to their names, be: 7,8,4,9,6 The data in the given form is known as raw data. The above given data can be placed in the bar chart as shown below: Name Marks Akshay 7 Maya 8 Dhanvi 4 Jaslen 9 Muskan 6

A histogram is the graphical representation of data. It is similar to the appearance of a bar graph but there is a lot of difference between histogram and bar graph because a bar graph helps to measure the frequency of categorical data. A categorical data means it is based on two or more categories like gender, months, etc. Whereas histogram is used for quantitative data.

For example:

The graph which uses lines and points to present the change in time is known as a line graph. Line graphs can be based on the number of animals left on earth, the increasing population of the world day by day, or the increasing or decreasing the number of bitcoins day by day, etc. The line graphs tell us about the changes occurring across the world over time. In a  line graph, we can tell about two or more types of changes occurring around the world.

For Example:

Pie chart is a type of graph that involves a structural graphic representation of numerical proportion. It can be replaced in most cases by other plots like a bar chart, box plot, dot plot, etc. As per the research, it is shown that it is difficult to compare the different sections of a given pie chart, or if it is to compare data across different pie charts.

Frequency Distribution Table

A frequency distribution table is a chart that helps us to summarise the value and the frequency of the chart. This frequency distribution table has two columns, The first column consist of the list of the various outcome in the data, While the second column list the frequency of each outcome of the data. By putting this kind of data into a table it helps us to make it easier to understand and analyze the data. 

For Example: To create a frequency distribution table, we would first need to list all the outcomes in the data. In this example, the results are 0 runs, 1 run, 2 runs, and 3 runs. We would list these numerals in numerical ranking in the foremost queue. Subsequently, we ought to calculate how many times per result happened. They scored 0 runs in the 1st, 4th, 7th, and 8th innings, 1 run in the 2nd, 5th, and the 9th innings, 2 runs in the 6th inning, and 3 runs in the 3rd inning. We set the frequency of each result in the double queue. You can notice that the table is a vastly more useful method to show this data.  Baseball Team Runs Per Inning Number of Runs Frequency           0       4           1        3            2        1            3        1

Sample Questions

Question 1: Considering the school fee submission of 10 students of class 10th is given below:

In order to draw the bar graph for the data above, we prepare the frequency table as given below. Fee submission No. of Students Paid   6 Not paid    4 Now we have to represent the data by using the bar graph. It can be drawn by following the steps given below: Step 1: firstly we have to draw the two axis of the graph X-axis and the Y-axis. The varieties of the data must be put on the X-axis (the horizontal line) and the frequencies of the data must be put on the Y-axis (the vertical line) of the graph. Step 2: After drawing both the axis now we have to give the numeric scale to the Y-axis (the vertical line) of the graph It should be started from zero and ends up with the highest value of the data. Step 3: After the decision of the range at the Y-axis now we have to give it a suitable difference of the numeric scale. Like it can be 0,1,2,3…….or 0,10,20,30 either we can give it a numeric scale like 0,20,40,60… Step 4: Now on the X-axis we have to label it appropriately. Step 5: Now we have to draw the bars according to the data but we have to keep in mind that all the bars should be of the same length and there should be the same distance between each graph

Question 2: Watch the subsequent pie chart that denotes the money spent by Megha at the funfair. The suggested colour indicates the quantity paid for each variety. The total value of the data is 15 and the amount paid on each variety is diagnosed as follows:

Chocolates – 3

Wafers – 3

Toys – 2

Rides – 7

To convert this into pie chart percentage, we apply the formula:  (Frequency/Total Frequency) × 100 Let us convert the above data into a percentage: Amount paid on rides: (7/15) × 100 = 47% Amount paid on toys: (2/15) × 100 = 13% Amount paid on wafers: (3/15) × 100 = 20% Amount paid on chocolates: (3/15) × 100 = 20 %

Question 3: The line graph given below shows how Devdas’s height changes as he grows.

Given below is a line graph showing the height changes in Devdas’s as he grows. Observe the graph and answer the questions below.

(i) What was the height of  Devdas’s at 8 years? Answer: 65 inches (ii) What was the height of  Devdas’s at 6 years? Answer:  50 inches (iii) What was the height of  Devdas’s at 2 years? Answer: 35 inches (iv) How much has  Devdas’s grown from 2 to 8 years? Answer: 30 inches (v) When was  Devdas’s 35 inches tall? Answer: 2 years.

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How exactly are data types represented in a computer?

I'm a beginning programmer reading K&R, and I feel as if the book assumes a lot of previous knowledge. One aspect that confuses me is the actual representation, or should I say existence, of variables in memory. What exactly does a data type specify for a variable? I'm not too sure of how to word this question... but I'll ask a few questions and perhaps someone can come up with a coherent answer for me.

When using getchar(), I was told that it is better to use type "int" than type "char" due to the fact that "int" can hold more values while "char" can hold only 256 values. Since we may need the variable to hold the EOF value, we will need more than 256 or the EOF value will overlap with one of the 256 characters. In my mind, I view this as a bunch of boxes with empty holes. Could someone give me a better representation? Do these "boxes" have index numbers? When EOF overlaps with a value in the 256 available values, can we predict which value it will overlap with?

Also, does this mean that the data type "char" is only fine to use when we are simply assigning a value to a variable manually, such as char c = 'a', when we definitely know that we will only have 256 possible ASCII characters?

Also, what is the actual important difference between "char" and "int"? If we can use "int" type instead of "char" type, why do we decide to use one over the other at certain times? Is it to save "memory" (I use quotes as I do not actually how "memory" exactly works).

Lastly, how exactly is the 256 available values of type char obtained? I read something about modulo 2^n, where n = 8, but why does that work (something to do with binary?). What is the modulo portion of "modulo 2^n" mean (if it has any relevance to modular arithmetic, I can't see the relation...)?

• kernighan-and-ritchie

• "when we definitely know that we will only have 256 possible ASCII characters?" nit-pick: There's only 128 characters in ASCII. –  kusma Commented Jan 9, 2010 at 17:29
• 1 there is more than just "int".. there is unsigned int (0-65535) and signed int (-32767 to 32767)... plain char in most implementations is 0 to 255 in unsigned. You also have short and long. short is two bytes, int is 4 bytes, and long is 8 bytes. See here: home.att.net/~jackklein/c/inttypes.html –  user195488 Commented Jan 9, 2010 at 17:29
• Sorry :s Then could I ask why we cannot use the 256 available values of type "char" if we are also using the function getchar() and expecting an EOF at some point? –  withchemicals Commented Jan 9, 2010 at 17:30
• 1 withchemicals: Because "char" doesn't really imply "ASCII". In C, "char" implies "smallest addressable piece of memory", otherwise known as "byte". getchar() simply gives you a byte from a stream (or EOF). –  kusma Commented Jan 9, 2010 at 17:41
• 2 Many of the answers below assume two's complement representation of numbers. C makes no such guarantees. It can run (and does run) on ones' complement machines, and sign-magnitude machines (or any other weird encodings there are!). –  Alok Singhal Commented Jan 10, 2010 at 2:51

11 Answers 11

Great questions. K&R was written back in the days when there was a lot less to know about computers, and so programmers knew a lot more about the hardware. Every programmer ought to be familiar with this stuff, but (understandably) many beginning programmers aren't.

At Carnegie Mellon University they developed an entire course to fill in this gap in knowledge, which I was a TA for. I recommend the textbook for that class: "Computer Systems: A Programmer's Perspective" http://amzn.com/013034074X/

The answers to your questions are longer than can really be covered here, but I'll give you some brief pointers for your own research.

Basically, computers store all information--whether in memory (RAM) or on disk--in binary, a base-2 number system (as opposed to decimal, which is base 10). One binary digit is called a bit. Computers tend to work with memory in 8-bit chunks called bytes.

A char in C is one byte. An int is typically four bytes (although it can be different on different machines). So a char can hold only 256 possible values, 2^8. An int can hold 2^32 different values.

For more, definitely read the book, or read a few Wikipedia pages:

• http://en.wikipedia.org/wiki/Binary_numeral_system
• http://en.wikipedia.org/wiki/Twos_complement

Best of luck!

UPDATE with info on modular arithmetic as requested:

First, read up on modular arithmetic: http://en.wikipedia.org/wiki/Modular_arithmetic

Basically, in a two's complement system, an n-bit number really represents an equivalence class of integers modulo 2^n.

If that seems to make it more complicated instead of less, then the key things to know are simply:

• An unsigned n-bit number holds values from 0 to 2^n-1. The values "wrap around", so e.g., when you add two numbers and get 2^n, you really get zero. (This is called "overflow".)
• A signed n-bit number holds values from -2^(n-1) to 2^(n-1)-1. Numbers still wrap around, but the highest number wraps around to the most negative, and it starts counting up towards zero from there.

So, an unsigned byte (8-bit number) can be 0 to 255. 255 + 1 wraps around to 0. 255 + 2 ends up as 1, and so forth. A signed byte can be -128 to 127. 127 + 1 ends up as -128. (!) 127 + 2 ends up as -127, etc.

• Thanks! Could you explain the "modulo" portion of 2^n? –  withchemicals Commented Jan 9, 2010 at 17:51
• I would rather have said "back in the days when programming was a lot lower level, closer to the hardware, so learning programming quickly required (and resulted in) a good basic understanding of the underlying hardware". –  L. Cornelius Dol Commented Jan 9, 2010 at 18:55
• Software Monkey: well-said, I think that's more exact than what I wrote. –  jasoncrawford Commented Jan 10, 2010 at 2:25
• withchemicals: Updated answer with some info on modular arithmetic; hope this helps. –  jasoncrawford Commented Jan 10, 2010 at 2:38
• BTW, on some platforms there is at least one character in the C character set whose value exceeds the maximum value for a signed char. For example, in EBCDIC, '0' is 0xF0. On such machines, 'char' must be unsigned. On some other platforms (e.g. some DSP's), sizeof(char)==sizeof(int), and both are able to hold values -32767..32767 (and perhaps other values as well). On such machines, 'char' must be signed. Note further that on such machines it would be possible for -1 to be a valid character value, and for EOF to be some value other than -1. –  supercat Commented Feb 15, 2011 at 20:41

One aspect that confuses me is the actual representation, or should I say existence, of variables in memory. What exactly does a data type specify for a variable?

At the machine level, the difference between int and char is only the size, or number of bytes, of the memory allocated for it by the programming language. In C, IIRC, a char is one byte while an int is 4 bytes. If you were to "look" at these inside the machine itself, you would see a sequence of bits for each. Being able to treat them as int or char depends on how the language decides to interpret them (this is also why its possible to convert back and forth between the two types).

When using getchar(), I was told that it is better to use type "int" than type "char" due to the fact that "int" can hold more values while "char" can hold only 256 values.

This is because there are 2^8, or 256 combinations of 8 bits (because a bit can have two possible values), whereas there are 2^32 combinations of 32 bits. The EOF constant (as defined by C) is a negative value, not falling within the range of 0 and 255. If you try to assign this negative value to a char (this squeezing its 4 bytes into 1), the higher-order bits will be lost and you will end up with a valid char value that is NOT the same as EOF. This is why you need to store it into an int and check before casting to a char.

Also, does this mean that the data type "char" is only fine to use when we are simply assigning a value to a variable manually, such as 0char c = 'a', when we definitely know that we will only have 256 possible ASCII characters?

Yes, especially since in that case you are assigning a character literal.

Also, what is the actual important difference between "char" and "int"? If we can use "int" type instead of "char" type, why do we decide to use one over the other at certain times?

Most importantly, you would pick int or char at the language level depending on whether you wanted to treat the variable as a number or a letter (to switch, you would need to cast to the other type). If you wanted an integer value that took up less space, you could use a short int (which I believe is 2 bytes), or if you were REALLY concerned with memory usage you could use a char , though mostly this is not necessary.

Edit : here's a link describing the different data types in C and modifiers that can be applied to them. See the table at the end for sizes and value ranges.

• Nitpick: to handle characters you'd stay the hell away from char and use a higher-level abstraction from a library like GLib. –  Tobu Commented Jan 9, 2010 at 17:34
• 2 Sure, but I still think its important to understand what's actually going on at the lower levels. –  danben Commented Jan 9, 2010 at 17:36
• 2 In C, an int can be 4 bytes, or more, or less. int must be able to represent values between -32767 and +32767 . –  Alok Singhal Commented Jan 9, 2010 at 17:40
• 3 int is not necessary 4 bytes. All C says is: short <= int <= long and short >= 2 bytes and long >= 4 bytes. See "The C Programming Language", ANSI C Version, by K&R, page 36. –  Dave O. Commented Jan 9, 2010 at 17:49
• 2 Also, in C, char may be signed, in which case it can store EOF , but of course char may be unsigned as well, and that's why we use int in this case. –  Alok Singhal Commented Jan 9, 2010 at 17:50

Basically, system memory is one huge series of bits, each of which can be either "on" or "off". The rest is conventions and interpretation.

First of all, there is no way to access individual bits directly; instead they are grouped into bytes, usually in groups of 8 (there are a few exotic systems where this is not the case, but you can ignore that for now), and each byte gets a memory address. So the first byte in memory has address 0, the second has address 1, etc.

A byte of 8 bits has 2^8 possible different values, which can be interpreted as a number between 0 and 255 (unsigned byte), or as a number between -128 and +127 (signed byte), or as an ASCII character. A variable of type char per C standard has a size of 1 byte.

But bytes are too small for a lot of things, so other types have been defined that are larger (i.e. they consist of multiple bytes), and CPUs support these different types through special hardware constructs. An int is typically 4 bytes nowadays (though the C standard does not specify it and ints can be smaller or bigger on different systems) because 4 bytes are 32 bits, and until recently that was what mainstream CPUs supported as their "word size".

So a variable of type int is 4 bytes large. That means when its memory address is e.g. 1000, then it actually covers the bytes at addresses 1000, 1001, 1002, and 1003. In C, it is possible to address those individual bytes as well at the same time, and that is how variables can overlap.

As a sidenote, most systems require larger types to be "word-aligned", i.e. their addresses have to be multiples of the word size, because that makes things easier for the hardware. So it is not possible to have an int variable start at address 999, or address 17 (but 1000 and 16 are OK).

• 1 Again, int may be 4 bytes or 2 or even 1, or anything. It must be able to represent the range +-32767. –  Alok Singhal Commented Jan 9, 2010 at 17:52
• wouldn't it be 2^7 and not 2^8? –  user195488 Commented Jan 9, 2010 at 17:57
• @Alok, yes that's what I say one paragraph higher. @Roboto: Nope. 8 bits means 2^8 different values. One bit has 2 values (2^1), each additional bit doubles this. –  Michael Borgwardt Commented Jan 9, 2010 at 18:06

I'm not going to completely answer Your question, but I would like to help You understand variables, as I had the same problems understanding them, when I began to program by myself.

For the moment, don't bother with the electronic representation of variables in memory. Think of memory as a continuous block of 1-byte-cells, each storing an bit-pattern (consisting of 0s and 1s).

By solely looking at the memory, You can't determine, what the bits in it represent! They are just arbitrary sequences of 0s and 1s. It is YOU, who specifies, HOW to interpret those bit patterns! Take a look at this example:

You could have written the following as well:

In both cases, the variables a, b and c are stored somewhere in the memory (and You can't tell their type). Now, when the compiler compiles Your code (that is translating Your program into machine instructions), it makes sure, to translate the "+" into integer_add in the first case and float_add in the second case, thus the CPU will interpret the bit patterns correctly and perform, what You desired.

Variable types are like glasses , that let the CPU look at a bit patterns from different perspectives.

To go deeper, I'd highly recommend Charles Petzold's excellent book " Code "

It covers more than what you ask, all of which leads to a better understanding of what's actually happening under the covers.

Really, datatypes are an abstraction that allows your programming language to treat a few bytes at some address as some kind of numeric type. Consider the data type as a lens that lets you see a piece of memory as an int, or a float. In reality, it's all just bits to the computer.

• The OP framed it in terms of hardware, but I agree with you; the individual questions were all better answered with a short introduction to type theory. –  Tobu Commented Feb 27, 2011 at 17:04
• In C, EOF is a "small negative number".
• In C, char type may be unsigned, meaning that it cannot represent negative values.
• For unsigned types, when you try to assign a negative value to them, they are converted to an unsigned value. If MAX is the maximum value an unsigned type can hold, then assigning -n to such a type is equivalent to assigning MAX - (n % MAX) + 1 to it. So, to answer your specific question about predicting, "yes you can". For example, let's say char is unsigned, and can hold values 0 to 255 inclusive. Then assigning -1 to a char is equivalent to assigning 255 - 1 + 1 = 255 to it.

Given the above, to be able to store EOF in c , c can't be char type. Thus, we use int , because it can store "small negative values". Particularly, in C, int is guaranteed to store values in the range -32767 and +32767 . That is why getchar() returns int .

If you are assigning values directly, then the C standard guarantees that expressions like 'a' will fit in a char . Note that in C, 'a' is of type int , not char, but it's okay to do char c = 'a' , because 'a' is able to fit in a char type.

About your question as to what type a variable should hold, the answer is: use whatever type that makes sense. For example, if you're counting, or looking at string lengths, the numbers can only be greater than or equal to zero. In such cases, you should use an unsigned type. size_t is such a type.

Note that it is sometimes hard to figure out the type of data, and even the "pros" may make mistakes. gzip format for example, stores the size of the uncompressed data in the last 4 bytes of a file. This breaks for huge files > 4GB in size, which are fairly common these days.

You should be careful about your terminology. In C, a char c = 'a' assigns an integer value corresponding to 'a' to c , but it need not be ASCII. It depends upon whatever encoding you happen to use.

About the "modulo" portion, and 256 values of type char : if you have n binary bits in a data type, each bit can encode 2 values: 0 and 1. So, you have 2*2*2...*2 ( n times) available values, or 2 n . For unsigned types, any overflow is well-defined, it is as if you divided the number by (the maximum possible value+1), and took the remainder. For example, let's say unsigned char can store values 0..255 (256 total values). Then, assigning 257 to an unsigned char will basically divide it by 256, take the remainder (1), and assign that value to the variable. This relation holds true for unsigned types only though. See my answer to another question for more.

Finally, you can use char arrays to read data from a file in C, even though you might end up hitting EOF , because C provides other ways of detecting EOF without having to read it in a variable explicitly, but you will learn about it later when you have read about arrays and pointers (see fgets() if you're curious for one example).

According to "stdio.h" getchars() return value is int and EOF is defined as -1. Depending on the actual encoding all values between 0..255 can occur, there for unsigned char is not enough to represent the -1 and int is used. Here is a nice table with detailed information http://en.wikipedia.org/wiki/ISO/IEC_8859

The beauty of K&R is it's conciseness and readability, writers always have to make concessions for their goals; rather than being a 2000 page reference manual it serves as a basic reference and an excellent way to learn the language in general. I recommend Harbinson and Steele "C: A Reference Manual" for an excellent C reference book for details, and the C standard of course.

You need to be willing to google this stuff. Variables are represented in memory at specific locations and are known to the program of which they are a part of within a given scope. A char will typically be stored in 8 bits of memory (on some rare platforms this isn't necessarily true). 2^8 represents 256 distinct posibilities for variables. Different CPU/compilers/etc represent the basic types int, long of varying sizes. I think the C standard might specify minimum sizes for these, but not maximum sizes. I think for double it specifies at least 64 bits, but this doesn't preclude intel from using 80 bits in a floating point unit. Anyway, typical sizes in memory on 32bit intel platforms would be 32 bits (4 bytes) for unsigned/signed int and float, 64 bits (8 bytes) for double, 8 bits for char (signed/unsigned). You should also look up memory alignment if you are really interested on the topic. You can also at the exact layout in your debugger by getting the address of your variable with the "&" operator and then peeking at that address. Intel platforms may confuse you a little when looking at values in memory so please look up little endian/big endian as well. I am sure stack overflow has some good summaries of this as well.

All of the characters needed in a language are respresented by ASCII and Extended ASCII. So there is no character beyond the Extended ASCII.

While using char, there is probability of getting garbage value as it directly stores the character but using int, there is less probability of it as it stores the ASCII value of the character.

For your last question about modulo:

Lastly, how exactly is the 256 available values of type char obtained? I read something about modulo 2^n, where n = 8, but why does that work (something to do with binary?). What is the modulo portion of "modulo 2^n" mean (if it has any relevance to modular arithmetic, I can't see the relation...)?

Think about modulo as a clock, where adding hours eventually results in you starting back at 0. Adding an hour for each step, you go from 00:00 to 01:00 to 02:00 to 03:00 to ... to 23:00 and then add one more hour to get back to 00:00. The "wrap-around" or "roll-over" is called modulo, and in this case is modulo 24.

With modulo, that largest number is never reached; as soon as you "reach" that number, the number wraps around to the beginning (24:00 is really 00:00 in the time example).

As another example, modern humanity's numbering system is Base 10 (i.e., Decimal), where we have digits 0 through 9. We don't have a singular digit that represents value 10. We need two digits to store 10.

Let's say we only have a one-digit adder, where the output can only store a single digit. We can add any two single-digit numbers together, like 1+2 , or 5+4 . 1+2=3 , as expected. 5+4=9 , as expected. But what happens if we add 5+5 or 9+1 or 9+9? To calculate 5+5 , our machine computes 10 , but it can't store the 1 due to its lack of memory capabilities, so the computer treats the 1 as an "overflow digit" and throws it away, only storing the 0 as the result. So, looking at your output for the computation 5+5 , you see the result is 0 , which probably isn't what you were expecting. To calculate 9+9 , your single-digit adding machine would correctly calculate 18 , but, it again, due to hardware memory limitations of storing a maximum of one digit, doesn't have the ability to store the 1 , so it throws it away. The adder CAN however store the 8 , so your result of 9+9 produces 8 .Your single-digit adder is modulo'ing by 10. Notice how you can never reach the number 10 in your output, even when your result should be 10 or bigger. The same issue occurs in binary, but with different modulo values.

As an aside, this "overflow" issue is especially bad with multiplication since you need twice the length of your biggest input to multiply two numbers (whether the numbers are binary or decimal or some other standard base) with all the result's digits intact. I.e., if you're multiplying a 32-bit number by another 32-bit number, your result might take 64 bits of memory instead of a convenient 32! E.g., 999 (3 digit input) times 999 (3 digit input) = 998,001 (6 digit output). Notice how the output requires double the number of digits of storage compared to one of the inputs' lengths (number of digits).

Back to binary modulo, A char in the programming language C is defined as the smallest accessible unit (source: I made it up based off what I've been told a hundred times). AFAIK, a single char is always the length of a single Byte. A byte is 8 bits, which is to say, a byte is an ordered group of eight 1s and/or 0s. E.g., 11001010 is a byte. Again, the order matters, meaning that 01 is not the same as 10, much like how 312 is not the same as 321 in Base 10.

Each bit you add gives you twice as many possible states. With 1 bit, you have 2^ 1 = 2 possible states (0,1). With 2 bits, you have 2^ 2 = 4 states (00,01,10,11), With 3 bits, you have 2^ 3 = 8 states (000,001,010,011,100,101,110,111). With 4 bits, you have 2^4 = 16 states, etc. With 8 bits (the length of a Byte, and also the length of a char), you have 2^ 8 = 256 possible states.

The largest value you can store in a char is 255 because a char has only 8 bits, meaning you can store all 1s to get the maximum value, which will be 11111111(bin) = 255(dec). As soon as you try to store a larger number, like by adding 1, we get the same overflow issue mentioned in the 1-digit adder example. 255+1 = 256 = 1 0000 0000 (spaces added for readability). 256 takes 9 bits to represent, but only the lower 8 bits can be stored since we're dealing with chars, so the most significant bit (the only 1 in the sequence of bits) gets truncated and we're left with 0000 0000 = 0. We could've added any number to the char, but the resulting char will always be between values 0 (all bits are 0s) and 255 (all bits are 1s).

Since a maximum value of 255 can be stored, we can say that operations that output/result in a char are mod256 (256 can never be reached, but everything below that value can (see the clock example)). Even if we add a million to a char, the final result will be between 0 and 255 (after a lot of truncation happens). Your compiler may give you a warning if you do a basic operation that causes overflow, but don't depend on it.

I said earlier that char can store up to 256 values, 0 through 255 - this is only partially true. You might notice that you get strange numbers when you try to do operations like char a = 255; .Printing out the number as an integer ( char a = 128; printf("%d",a); ) should tell you that the result is -128. Did the computer think I added a negative by accident? No. This happened because a char is naturally signed, meaning it's able to be negative. 128 is actually overflow because the range of 0 to 255 is split roughly in half, from -128 to +127. The maximum value being +127, and then adding 1 to reach 128 (which makes it overflow by exactly 1) tells us that the resulting number of char a = 128; will be the minimum value a char can store, which is -128. If we had added 2 instead of 1 (like if we tried to do char a = 129; ), then it would overflow by 2, meaning the resulting char would have stored -127. The maximum value will always wrap around to the minimum value in non-floating point numbers.

• Floating-point numbers still work based on place values (but it's called a mantissa and functions differently) like ints, shorts, chars, and longs, but floating-point numbers also have a dedicated sign bit (which has no additive value) and an exponent.

If you choose to look at the raw binary when setting variables equal to literal values like 128 or -5000

For signed non-floating-point numbers, the largest place value get assigned a 1 when the overall number is negative, and that place value gets treated as a negative version of that typical place value. E.g., -5 (Decimal) would be 1xx...x in binary (where each x is a placeholder for either a 0 or 1). As another example, instead of place values being 8,4,2,1 for an unsigned number, they become -8,4,2,1 for a signed number, meaning you now have a "negative 8's place".

2's Complement to switch between + and - values : Flip (i.e., "Complement") all bits (i.e., each 1 gets flipped to a 0, and, simultaneously, each 0 gets flipped to a 1)(e.g., -12 = -16 + 4 = 10100 -> 01011). After flipping, add value 1 (place value of 1). (e.g., 01011 + 1 = 01100 = 0+8+4+0+0 = +12). Summary: Flip bits, then add 1.

Examples of using 2's Complement to convert binary numbers into EQUIVALENT signed decimal numbers :

• 11 = (-2)+1 = -1
• 111 = (-4)+2+1 = -1
• 1111 = (-8)+4+2+1 = -1
• 1000 = (-8)+0+0+0 = -8
• 0111 = 0+4+2+1 = 7
• Notice how 0111 and 111 are treated differently when they're designated as "signed" numbers (instead of "unsigned" (always positive) numbers). Leading 0s are important.

If you see the binary number 1111, you might think, "Oh, that's 8+4+2+1 = 15". However, you don't have enough information to assume that. It could be a negative number. If you see "(signed) 1111", then you still don't know the number for certain due to One's Complement existing, but you can assume it means "(signed 2's Complement) 1111", which would be (-8)+4+2+1 = -1. The same sequence of bits, 1111, can be interpreted as either -1 or 15, depending on its signedness. This is why the unsigned keyword in unsigned char is important. When you write char , you are implicitly telling the computer that you want a signed char.

• unsigned char - Can store numbers between 0 and 255
• (signed) char - Can store number between -128 and +127 (same span, but shifted to allow negatives)

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Representation of Data/Information

Computers do not understand human language; they understand data within the prescribed form. Data representation is a method to represent data and encode it in a computer system. Generally, a user inputs numbers, text, images, audio, and video etc types of data to process but the computer converts this data to machine language first and then processes it.

Some Common Data Representation Methods Include

Data representation plays a vital role in storing, process, and data communication. A correct and effective data representation method impacts data processing performance and system compatibility.

Computers represent data in the following forms

Number system.

A computer system considers numbers as data; it includes integers, decimals, and complex numbers. All the inputted numbers are represented in binary formats like 0 and 1. A number system is categorized into four types −

• Binary − A binary number system is a base of all the numbers considered for data representation in the digital system. A binary number system consists of only two values, either 0 or 1; so its base is 2. It can be represented to the external world as (10110010) 2 . A computer system uses binary digits (0s and 1s) to represent data internally.
• Octal − The octal number system represents values in 8 digits. It consists of digits 0,12,3,4,5,6, and 7; so its base is 8. It can be represented to the external world as (324017) 8 .
• Decimal − Decimal number system represents values in 10 digits. It consists of digits 0, 12, 3, 4, 5, 6, 7, 8, and 9; so its base is 10. It can be represented to the external world as (875629) 10 .

The below-mentioned table below summarises the data representation of the number system along with their Base and digits.

Bits and Bytes

A bit is the smallest data unit that a computer uses in computation; all the computation tasks done by the computer systems are based on bits. A bit represents a binary digit in terms of 0 or 1. The computer usually uses bits in groups. It's the basic unit of information storage and communication in digital computing.

A group of eight bits is called a byte. Half of a byte is called a nibble; it means a group of four bits is called a nibble. A byte is a fundamental addressable unit of computer memory and storage. It can represent a single character, such as a letter, number, or symbol using encoding methods such as ASCII and Unicode.

Bytes are used to determine file sizes, storage capacity, and available memory space. A kilobyte (KB) is equal to 1,024 bytes, a megabyte (MB) is equal to 1,024 KB, and a gigabyte (GB) is equal to 1,024 MB. File size is roughly measured in KBs and availability of memory space in MBs and GBs.

The following table shows the conversion of Bits and Bytes −

A Text Code is a static code that allows a user to insert text that others will view when they scan it. It includes alphabets, punctuation marks and other symbols. Some of the most commonly used text code systems are −

Extended ASCII

EBCDIC stands for Extended Binary Coded Decimal Interchange Code. IBM developed EBCDIC in the early 1960s and used it in their mainframe systems like System/360 and its successors. To meet commercial and data processing demands, it supports letters, numbers, punctuation marks, and special symbols. Character codes distinguish EBCDIC from other character encoding methods like ASCII. Data encoded in EBCDIC or ASCII may not be compatible with computers; to make them compatible, we need to convert with systems compatibility. EBCDIC encodes each character as an 8-bit binary code and defines 256 symbols. The below-mentioned table depicts different characters along with their EBCDIC code.

ASCII stands for American Standard Code for Information Interchange. It is an 8-bit code that specifies character values from 0 to 127. ASCII is a standard for the Character Encoding of Numbers that assigns numerical values to represent characters, such as letters, numbers, exclamation marks and control characters used in computers and communication equipment that are using data.

ASCII originally defined 128 characters, encoded with 7 bits, allowing for 2^7 (128) potential characters. The ASCII standard specifies characters for the English alphabet (uppercase and lowercase), numerals from 0 to 9, punctuation marks, and control characters for formatting and control tasks such as line feed, carriage return, and tab.

Extended American Standard Code for Information Interchange is an 8-bit code that specifies character values from 128 to 255. Extended ASCII encompasses different character encoding normal ASCII character set, consisting of 128 characters encoded in 7 bits, some additional characters that utilise full 8 bits of a byte; there are a total of 256 potential characters.

Different extended ASCII exist, each introducing more characters beyond the conventional ASCII set. These additional characters may encompass symbols, letters, and special characters to a specific language or location.

Extended ASCII Tabular column

It is a worldwide character standard that uses 4 to 32 bits to represent letters, numbers and symbols. Unicode is a standard character encoding which is specifically designed to provide a consistent way to represent text in nearly all of the world's writing systems. Every character is assigned a unique numeric code, program, or language. Unicode offers a wide variety of characters, including alphabets, ideographs, symbols, and emojis.

Unicode Tabular Column

The Mixed Methods Blog

How many students are taking dual enrollment courses in high school new national, state, and college-level data.

Last week, the U.S. Department of Education released new data that, for the first time ever, provide college-level counts of the number of high school dual enrollment students, disaggregated by race/ethnicity and gender. The provisional release of these new data represents years of effort among dozens of organizations pushing for better dual enrollment data. In this post, I detail a first look at this new information.

What is the size and significance of dual enrollment across postsecondary sectors and states?

Nationally, community colleges enrolled the majority of high school dual enrollment students, followed by public four-year and private nonprofit four-year colleges. For community colleges, the 1.78 million high school dual enrollment students represented 21% of total enrollments during the 2022-23 year (8.6 million in total). Two hundred forty thousand high school students took dual enrollment at the 10 largest dual enrollment colleges alone, and of these top 10, eight were community colleges.

As shown below, the size of high school dual enrollment at community colleges differed substantially across states. For example, in Idaho and Indiana, high schoolers represented the majority of community college enrollments in 2022-23, and in eight other states dual enrollment made up a third or more of total community college enrollment. At 37 community colleges across the country, 50% or more of enrollment was from high school dual enrollment.

Compared to undergraduate students overall, how representative are dual enrollment students by race/ethnicity and gender?

Compared to undergraduates overall, Black and Hispanic students were underrepresented nationally in dual enrollment during 2022-23, echoing our previous analysis of national K-12 data. White students were overrepresented in dual enrollment, accounting for 52% of high school dual enrollment compared to 45% of undergraduate enrollment overall (and 44% of K-12 enrollment).

Black students, which made up 13% of undergraduate enrollment and 15% of public K-12 enrollment, comprised only 8% of high school dual enrollment. Black students were underrepresented in dual enrollment in every state except for Massachusetts. And Black students had equal or greater representation in dual enrollment at only 74 community colleges—fewer than one in ten community colleges serving dual enrollment students nationally.

Hispanic/Latino students made up 22% of undergraduate enrollment (and 29% of public K-12 enrollment) but only 20% of high school dual enrollment. Hispanic/Latino students had greater or equal representation in dual enrollment in 18 states and at more than a third of community colleges nationally.

One caveat is that, nationally, more dual enrollment students were reported with unknown race/ethnicity (9%) compared to undergraduates overall (5%), muddying the picture somewhat. Similar to undergraduates overall, men were underrepresented among dual enrollment students nationally (43%).

In the dashboard below, you can select your college or your state and identify the number of dual enrollment students, consider the size of dual enrollment as a percentage of overall undergraduate enrollment, and compare the racial/ethnic and gender representation of dual enrollment students to that of undergraduate enrollments overall.

How does your state compare to others in dual enrollment size and representation?

The top five states for dual enrollment by size—California, Texas, New York, Indiana, and Florida—together reported nearly 900,000 dual enrollments, about a third of dual enrollment nationally. California, Texas, and Florida enrolled the largest numbers of Hispanic or Latino dual enrollment students, and Texas, Florida, and Georgia enrolled the largest numbers of Black dual enrollment students.

In the dashboard below, you can look across states to compare the percentage of dual enrollment as a share of overall undergraduate enrollment (shown in the map), see states ranked in order of the number of high schoolers enrolled in dual enrollment, and compare racial/ethnic composition of dual enrollment across states and to the U.S. overall.

How does participation in dual enrollment vary among colleges in your state?

In the dashboard below, you can look within your state to compare the size and demographic breakdown of dual enrollment students across colleges. Select your state to view all of the postsecondary institutions, the size of their dual enrollment programs, the significance of dual enrollment as a share of their undergraduate headcount, and dual enrollment counts disaggregated by race/ethnicity and gender.

Implications of the new data

Given decades of research documenting the positive benefits of participating in dual enrollment coursework on high school and postsecondary outcomes, the growth of these programs has great potential to expand college and career opportunity for high school students across the country. And yet gaps in access to dual enrollment for Black, Hispanic, low-income, and other underserved groups persist in preventing these programs from fully realizing their potential. But, as we have learned in our dual enrollment equity pathways research, it is not only possible to broaden the benefits of dual enrollment but also increasingly important for college business models to rethink the conventional approach, sometimes described as “programs of privilege” or “random acts” of dual enrollment. These new data can help to motivate and guide reform efforts by providing public, college- and state-level, disaggregated data for practitioners and policymakers seeking to rethink dual enrollment as a more equitable and effective on-ramp to career-path postsecondary education for students.

About the author

John Fink is a senior research associate and program lead at the Community College Research Center.

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Data URLs , URLs prefixed with the data: scheme, allow content creators to embed small files inline in documents. They were formerly known as "data URIs" until that name was retired by the WHATWG.

Note: Data URLs are treated as unique opaque origins by modern browsers, rather than inheriting the origin of the settings object responsible for the navigation.

Data URLs are composed of four parts: a prefix ( data: ), a MIME type indicating the type of data, an optional base64 token if non-textual, and the data itself:

The mediatype is a MIME type string, such as 'image/jpeg' for a JPEG image file. If omitted, defaults to text/plain;charset=US-ASCII

If the data contains characters defined in RFC 3986 as reserved characters , or contains space characters, newline characters, or other non-printing characters, those characters must be percent-encoded .

If the data is textual, you can embed the text (using the appropriate entities or escapes based on the enclosing document's type). Otherwise, you can specify base64 to embed base64-encoded binary data. You can find more info on MIME types here and here .

A few examples:

The text/plain data Hello, World! . Note how the comma is percent-encoded as %2C , and the space character as %20 .

base64-encoded version of the above

An HTML document with <h1>Hello, World!</h1>

An HTML document with <script>alert('hi');</script> that executes a JavaScript alert. Note that the closing script tag is required.

Encoding data into base64 format

Base64 is a group of binary-to-text encoding schemes that represent binary data in an ASCII string format by translating it into a radix-64 representation. By consisting only of characters permitted by the URL syntax ("URL safe"), we can safely encode binary data in data URLs. Base64 uses the characters + and / , which may have special meanings in URLs. Because Data URLs have no URL path segments or query parameters, this encoding is safe in this context.

Encoding in JavaScript

The Web APIs have native methods to encode or decode to base64: Base64 .

Encoding on a Unix system

Base64 encoding of a file or string on Linux and macOS systems can be achieved using the command-line base64 (or, as an alternative, the uuencode utility with -m argument).

Encoding on Microsoft Windows

On Windows, Convert.ToBase64String from PowerShell can be used to perform the Base64 encoding:

Alternatively, a GNU/Linux shell (such as WSL ) provides the utility base64 :

Common problems

This section describes problems that commonly occur when creating and using data URLs.

This represents an HTML resource whose contents are:

The format for data URLs is very simple, but it's easy to forget to put a comma before the "data" segment, or to incorrectly encode the data into base64 format.

A data URL provides a file within a file, which can potentially be very wide relative to the width of the enclosing document. As a URL, the data should be formattable with whitespace (linefeed, tab, or spaces), but there are practical issues that arise when using base64 encoding .

Browsers are not required to support any particular maximum length of data. For example, the Opera 11 browser limited URLs to 65535 characters long which limits data URLs to 65529 characters (65529 characters being the length of the encoded data, not the source, if you use the plain data: , without specifying a MIME type). Firefox version 97 and newer supports data URLs of up to 32MB (before 97 the limit was close to 256MB). Chromium objects to URLs over 512MB, and Webkit (Safari) to URLs over 2048MB.

Invalid parameters in media, or typos when specifying 'base64' , are ignored, but no error is provided.

The data portion of a data URL is opaque, so an attempt to use a query string (page-specific parameters, with the syntax <url>?parameter-data ) with a data URL will just include the query string in the data the URL represents.

A number of security issues (for example, phishing) have been associated with data URLs, and navigating to them in the browser's top level. To mitigate such issues, top-level navigation to data: URLs is blocked in all modern browsers. See this blog post from the Mozilla Security Team for more details.

Specifications

Browser compatibility

BCD tables only load in the browser with JavaScript enabled. Enable JavaScript to view data.

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Berkshire Hathaway hits $1 trillion market capitalization

Aug. 28 (UPI) -- Billionaire Warren Buffett 's Berkshire Hathaway market capitalization surpassed the $1 trillion level for the first time Wednesday, according to Dow Jones Market Data.

Berkeshire joins just eight other companies at that level and is the only non-tech $1 trillion and above private-sector company. Advertisement

The other companies to have reached a $1 trillion market cap include Apple, Amazon , Microsoft, Tesla, Google parent company Alphabet, Meta, Nvidia and Saudi Aramco, owned by the Saudi Arabia government

Cathy Seifert, Berkshire analyst at CFRA Research, said the $1 trillion achievement "is a testament to the firm's financial strength and franchise value."

Buffett's company had a record $277 billion in cash in June, most of it invested in U..S. Treasury bonds. Berkshire owns more of those bonds than the U.S. Federal Reserve .

Unlike the tech companies in that $1 trillion club, Berkshire's focus is on older economy holdings like BNSF Railway, Geico Insurance and Dairy Queen.

When Buffett took control the company was a textile business in the 1960s. He expanded holdings to include railroad, energy, insurance and retail. Advertisement

Recently Buffett sold off about half of Berkshire's Apple investments.

Berkshire Class A shares have increased more than 28% since the first of the year. Class B shares have grown 30%.

The Class A shares were trading Wednesday at $696,442, according to FactSet data. Class B shares were at $464.33 Wednesday.

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Messer and Its Data-Driven Enterprise Bring “Gases for Life”

Since 1928, spectators at Macy’s Thanksgiving Day Parade have marveled at the iconic, giant balloons that drift through the streets of mid-town Manhattan. No party-store helium canister will do for these towering balloons, which often measure several stories high. Those gargantuan renditions of our favorite characters are all sent flying by Messer , a leader in the safe and reliable production and delivery of industrial and medical gases for more than 120 years.

Those gases also include oxygen, hydrogen, nitrogen, carbon dioxide, argon, neon, xenon, and krypton—all critical to supporting processes and products in electronics, food and beverage, metals, biopharmaceuticals, and other industries.

Business demands and market realities in the dynamic gas sector are constantly in flux, so Messer relies on real-time data intelligence to stay agile and flexible in their decision-making. Increasingly hampered by siloed data and a patchwork of third-party visualization tools, Messer embarked on a digital transformation to create a next-generation data management solution worthy of the company’s high-tech, high-flying operations.

Data with a Purpose

Messer knows critical and often lifesaving business decisions require accurate, real-time intelligence and insights. CIO David Johnston explained: “The stakes in many of the sectors that we provide gases for are really very high.”

From steel plants to the semiconductor industry to intensive care units, “it is critical that our distribution processes are operating at a level that ensures our customers are getting what they need when they need it.” 

Messer was able to rise to the moment and meet the urgent needs of its customers when the COVID-19 pandemic delivered unprecedented demand for oxygen coupled with massive logistical challenges. That global crisis revealed that Messer’s legacy IT system needed an overhaul.

Messer’s siloed data was in several different databases, which meant it was time-consuming to access, and a single source of the truth was elusive. Various visualization tools also required different data formats, which slowed reporting time and bogged the IT department as it tried to manage a complex, disparate landscape, creating, as Johnston explained, “a huge amount of complexity and a huge amount of inefficiency.”

Messer CIO David Johnston sought a solution that would provide a unified source of truth and the powerful analytics tools Messer needed to give an elevated purpose to the company’s data—a new, cloud-based data management and analytics foundation for an actual data-driven enterprise. SAP Business Technology Platform (SAP BTP) was the company’s choice.

The Modern Data Landscape Delivers

SAP BTP, with SAP Data Warehouse Cloud, SAP Analytics Cloud, and the next-generation SAP Datasphere, provided a modern data architecture to establish a single, trusted source of truth, combining 12 data sources in one solution for mission-critical business insights.

Messer has been reaping benefits across the board, from IT and supply chain cost savings to improved customer service, inventory management, and data security. “We started with five specific use cases that we went after,” Johnston shared. “As I sit here today, we’re at well over 200.”

Messer’s new, simplified IT landscape has empowered business users, who benefit from intuitive, self-service dashboards and quick access to relevant, actionable, real-time data, as well as IT personnel, to now focus on higher-value, strategic tasks. This amounts to accelerated time-to-insight and more energy and resources available to focus on future innovation.

“With a data fabric that allows us to see our business in a consistent, fast, reliable, and highly trustworthy way,” Johnston said, “what we can do is really almost unlimited.”

Next for Messer and Wise Advice with an Eye on AI

With Messer’s new, streamlined data management foundation, the sky is no longer the limit.

“Our objective isn’t just to deliver a suite of great dashboards and great analytics stories,” Johnston explained. “Our goal is to build out a strong, coherent, strategic data fabric that will allow us to unlock the power of AI and drive the next level of business transformation.”

For other organizations hoping to build the data foundation that will send them soaring into the future, ready to capitalize on artificial intelligence technologies and whatever else awaits, Johnston’s advice is to frame your technology transformation as a business transformation, and a business imperative.

“Bring the business community together around data,” he said. “All the key stakeholders, the influencers, and the owners of data from across the organization: bring them to the table.”

The Full Episode

Messer CIO David Johnston joined SAP BTP Better Together: Customer Conversations to discuss the medical and industrial gasses industry and Messer’s digital transformation.

• Thought Leadership Podcast : Johnston sat down with Thulium’s CEO Tamara McCleary to discuss why end-to-end data-driven insights are necessary, what technology solutions were required for the world’s largest privately owned industrial gases company to transform, and why Messer leveraged SAP BTP to drive a complete business transformation.
• Practitioners’ Video : Johnston and I discuss why and how Messer, one of the biggest suppliers of medical oxygen and other industrial mission-critical gases, built a new, cloud-based data management and analytics foundation because the future belongs to data-driven organizations, and thriving in the dynamic industrial gases sector means responding quickly to changing market conditions.

Explore more success stories of customers leveraging SAP BTP to drive transformation that overhauls legacy IT systems:

• DuluxGroup : How can an innovative cloud-based integration shape a modern and hybrid IT landscape?
• Lufthansa Group : Co-creating a data fabric infused with context and governance for accurate business-wide data-driven decision-making

For the full episode and the on-demand Better Together: Customer Conversations series, visit sap.com/btp . To share input on the topics and technologies you want us to cover, or if you are interested in being a guest on the show, email us .

Timo Elliott is vice president and global innovation advocate for SAP BTP at SAP.

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HomeMade: Self-Service Home Care Because There Is No Place Like Home

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Closing the gender and race gaps in North American financial services

At the beginning of 2021, women in North America remained dramatically underrepresented in the financial-services workforce—particularly at the level of senior management and above. A new industry-specific analysis of data from the latest Women in the Workplace report, a McKinsey collaboration with LeanIn.Org, reveals a leaky pipeline from which women are falling out in greater numbers as they progress up the career ladder, resulting in significant inequality at the top. Consistent with previous years, women in financial services continue to experience a “broken rung” at the first step from entry level to manager—where they are significantly less likely than men to be promoted (for more about our research, see sidebar “About the research and findings”). At the same time, women leaders have taken on the additional responsibilities of supporting employees and investing in diversity and inclusion during the COVID-19 pandemic—but they aren’t being rewarded for this critical work.

About the research and findings

For the past seven years, McKinsey and LeanIn.Org have tracked the progress of women in corporate America. The latest Women in the Workplace report , released in September 2021, is based on data from 423 employers across the United States and Canada as well as a survey of more than 65,000 people from 88 companies. All data were collected between May and August of 2021.

To learn more about the financial-services sector specifically, we carved out the employer data of 27 asset-management companies (excluding private equity), 25 banking and consumer-finance companies, ten insurers, and nine payments companies, which collectively employ over 500,000 employees. We also isolated 8,470 survey responses from employees in the financial sector. 1 Industry-specific n sizes may differ from the Women in the Workplace report because of differences in groupings for analysis.

As demands continue to escalate, it is no surprise that women in financial services are more likely than men to report feeling burned out. Yet women do not always feel that they can request the support they need, including the flexibility to work remotely. As financial-services firms plan for a return to the office, they need to do more to create an equal and inclusive workplace where all women of all backgrounds feel supported, valued, and recognized for the full extent of their contributions.

A leaky pipeline for women—especially women of color

At the beginning of 2021, the representation of women and women of color in the financial-services workforce had increased across all ranks above entry level, compared with 2018 . While women have a slight edge at the entry level (comprising 52 percent of the industry workforce), their representation falls off at every step of the corporate pipeline. This slide is particularly steep for women of color (Black, Latina, Asian 1 “Asian women” refers to women who self-identify as East Asian, South Asian, or Southeast Asian. ): from entry level to the C-suite, the representation of women of color falls by 80 percent.

The highest levels of corporate leadership are still dominated by men, though women have made notable gains in the past three years. During that time, the share of women grew by 40 percent at the senior-vice-president (SVP) level and 50 percent at the C-suite level—though this increase is off a low starting point. Despite progress, 64 percent of financial-services C-suite executives are still White men, and 23 percent are White women—leaving just 9 percent of C-suite positions held by men of color and 4 percent by women of color (Exhibit 1).

Gender and racial diversity look different by industry

The representation of women and women of color varies across the different industries that make up the financial-services workforce: asset management, banking, insurance, and payments (Exhibit 2).

Asset management. The asset-management industry lags behind financial services in the representation of women across most levels. 2 Our analysis of asset management excludes private-equity companies. Of particular concern is that the representation of women of color has not meaningfully changed since 2018—and has actually gone down at critical levels of the pipeline. For example, the share of women of color in entry-level roles has decreased slightly in the past three years.

Banking. Gender diversity in banking reflects the reality in financial services overall, with an even split between men and women at entry level that declines with each rung up the ladder. Women make up 53 percent of the entry-level banking workforce but less than one-third at the SVP and C-suite levels. Notably, nearly one in four employees at the entry level is a woman of color, though this falls to one in 20 at the C-suite level—on par with both the financial-services and cross-industry average.

Insurance. Insurance continues to lead in gender diversity within the entry-level workforce, where 66 percent are women—though these women are predominantly White. The high share of women at entry level is mostly due to the larger, more diverse workforces of call centers and field-claims organizations employed by the insurance industry. Black women comprise more than 7 percent of the entry-level workforce—the highest among financial-services industries. However, this number drops precipitously along the corporate ladder and falls to zero at the C-suite.

Payments. Within the payments industry, gender diversity varies significantly by job level. Payments has the lowest share of women in the entry-level, manager, and senior-manager ranks, but among the financial-services industry, it is the closest to gender parity in the C-suite (where 39 percent are women). Women of color make up 9 percent of the C-suite in the payments industry—the highest representation among all financial-services industries.

Intersectional differences within the ‘broken rung’

As in many other industries, women in financial services continue to experience a broken rung at the first step from entry level to manager—where they are significantly less likely than men to be promoted. That results in a long-term negative impact on women’s ability to progress through the talent pipeline. When women are not getting promoted at the junior levels of the pipeline, it is challenging to equalize gender diversity at more senior levels—the gap is simply too large to catch up.

Within financial services, only 86 women are promoted to manager for every 100 men, which is on par with the cross-industry Women in the Workplace  findings. In 2020, women of color were promoted at even higher rates than women overall: 93 women of color were promoted for every 100 men. While this is an encouraging sign of progress, a closer look reveals granular and marked differences between the experiences of Asian, Black, and Hispanic women across financial-services industries (Exhibit 3).

Women in financial services reported more support in the past year

Financial-services companies helped many employees weather the COVID-19 pandemic—seemingly at higher rates than corporate America overall. While 47 percent of women surveyed for the 2021 edition of the Women in the Workplace study reported receiving increased support in the past year, 59 percent of women in financial services reported the same. And about 28 percent of women overall reported additional holidays or paid time off, compared with 42 percent of women in financial services. This is partly because the financial-services industry was well-positioned to transition to remote work and was able to avoid the worst of the economic fallout from the pandemic.

These differences and others could help explain why women in financial services are slightly less likely to consider leaving their company; 28 percent said they would consider it, compared with 33 percent of women overall.

Demands on women continue to escalate—but recognition doesn’t

Women in dual-career households.

Women in financial services are more likely than men to be in a dual-career household. According to the survey, 62 percent of men are in a dual-career household, compared with 81 percent of women. Furthermore, women are much less likely than men to say that their career takes priority over their partner’s career (exhibit).

As the pandemic has stretched on, women’s outsize contribution to taking care of homes and families—often while maintaining their careers—has continued to grow. Senior-level women are 57 percent more likely than senior-level men to have a spouse who works full time. Of those who live with a spouse, senior-level women in financial services are seven and a half times more likely than their male peers to say they are responsible for all or most of household responsibilities. This figure has jumped significantly since 2018, when it was four times more likely (for more, see sidebar “Women in dual-career households”).

In addition to these home-based responsibilities, women are also stepping up in the workplace and setting a new standard for leadership. Across industries, women leaders are more active champions of diversity, equity, and inclusion (DE&I) initiatives than their male peers. In financial services, senior-level women in particular are much more likely to feel a personal responsibility to promote DE&I, which usually falls outside formal job responsibilities—increasing their invisible workload without increasing recognition.

Women in financial services are also doing more than their male peers to support their teams, especially in manager and entry-level roles. Eighty percent of women in financial services reported consistently providing emotional support for a team member in the past year, compared with 72 percent of men. Women managers in financial services are also slightly more likely than their male peers to say they set clear work-availability boundaries, ensure employees’ workloads are reasonable, and organize team-bonding events. Employees recognize this difference. Financial-services employees with women managers are 50 percent more likely to say their manager provided emotional support and 25 percent more likely to report that their manager has helped them navigate work–life challenges (Exhibit 4).

This supportive leadership is also modeled by entry-level women in financial services. Half of these women said they provided emotional support for a team member in the past year, while 38 percent of their male colleagues said the same. Entry-level women in financial services are also 2.6 times more likely than their male peers to organize team-bonding events. And yet entry-level men are 67 percent more likely than their women peers to say the work they do to support the people on their teams is formally recognized. In many ways, this emotional support has provided the connective tissue that has been so critical during the upheaval of the pandemic. When managers support employee well-being , employees report feeling happier, less burned out, and less likely to consider leaving their company.

In addition, more than half of women in financial services (53 percent) reported experiencing at least one microaggression (such as being interrupted or having their judgment questioned) over the past year. This is slightly lower than women in corporate America overall (58 percent) but still high. And in both corporate America overall and financial services specifically, women of color are more likely to experience microaggressions. These experiences can have a profoundly negative impact on an employee’s motivation, job satisfaction, stress level, and desire to stay at a company.

Indeed, the survey confirmed what many expect: all employees are more burned out this year. In financial services, this is especially pronounced at the senior level, with 48 percent of senior-level women having reported being burned out, compared with 41 percent of senior-level men. However, burnout is not only at the senior level; almost three in ten entry-level women in financial services say they are burned out often or almost always.

What do women need in the return to work?

Simply put, women need two elements for a successful return to work: flexibility and managerial support. Women want to continue to work remotely after the pandemic, and they don’t feel like remote work has caused them to miss out. Forty-five percent of women in financial services say they want to continue to work remotely, 3 Defined as working remotely 91 to 100 percent of the time. compared with 36 percent of men in finance. When it comes to the broader effect on their career of working remotely, both men and women in financial services generally agree on the extent to which their careers have stalled, lost ground, or advanced over the past year (Exhibit 5).

However, women report feeling less able to request remote work when needed. Men in financial services are 76 percent more likely than their women colleagues to say they have the flexibility to work remotely, and women are more than two times as likely to say they have almost no flexibility to work remotely (Exhibit 6). And 29 percent of men say it’s not a big deal to request opportunities in work flexibility, compared with 19 percent of women—likely because women report being more likely to feel like a burden or to worry about the request hurting their career.

Of course, a hybrid working model isn’t a silver bullet. Even though women managers are recognized as more supportive than male managers, women aren’t getting that support in return. Managerial support is a crucial, high-stakes priority for improving women’s experiences in the financial-services workforce.

The importance of flexible working arrangements and supportive managers will be key: almost one in four women in financial services say that offering more flexible hours and ensuring managers were supportive of employees could have helped avoid attrition or downshifting.

Taking action

It is clear that financial-services companies need to do more to address the disproportionate effects of the pandemic on women and pave the way for a more equal and inclusive workplace. Specifically, companies can focus on four priorities.

Fix the broken rung

Achieving gender diversity across the pipeline will require financial-services companies to address the unequal promotion rates from entry level to manager—the broken rung. One direct solution is maintaining gender balance in promotion slates. The broader Women in the Workplace survey  revealed that while a majority of companies require diverse slates of similarly qualified candidates in their hiring processes, only 23 percent of companies apply those same policies to their performance reviews. By doing so, companies can hold themselves accountable to progress on diversity—across both gender and race—at the manager level and above.

Furthermore, financial-services companies should investigate their performance-review and promotion processes for areas where conscious or unconscious bias may limit the advancement opportunities of women and women of color. This means evaluating employees based on outcomes instead of subjective inputs and ensuring that employees—and especially women—are not penalized for taking advantage of flexible work options.

Create a flexible and supportive culture

Of course, improving gender and racial diversity is only part of the broader DE&I mandate. Leaders—both men and women—of financial-services companies also need to purposefully foster an inclusive culture where women of all backgrounds feel that their managers respect and support their needs.

Women in financial services are more likely to want flexibility in their work arrangements but less likely to feel comfortable asking for it. Companies can lower the barriers by spotlighting senior leaders, particularly women, who take advantage of the flexible work options that the company offers to all employees. Leaders should set clear expectations around remote work and provide specific examples to illustrate accepted working norms. And because women often look to their managers to interpret formal and informal company policies, it is particularly important for managers to respect company-wide boundaries around flexible and remote work—and to role model these values themselves.

Grow and reward caring people leaders

Women in financial services do more to take care of their teams, yet they receive less support from their managers compared with men. Companies should take steps to educate and train managers on how to provide emotional support for their colleagues (for example, setting regular check-ins and creating space for honest conversations around well-being). Requiring participation or providing incentives to attend these training programs can help to encourage widespread adoption. The responsibility of managers to support employee well-being should be formalized in performance-evaluation criteria that explicitly reward caring people leadership. This would also ensure that managers who already carry much of this “invisible” workload—mostly women—are recognized for their contributions.

Actively monitor and solve for burnout

To combat higher levels of burnout among women, financial-services companies could train managers and employees on how to notice and intervene when team members are at risk of burning out. Managers should play an active role in encouraging employees to set boundaries (especially in remote or hybrid environments) and reduce the expectation of being “always on.” The responsibility falls not only on direct managers but also on the entire company to provide adequate mental-health resources to employees and nurture a culture where everyone is willing to raise their hands and acknowledge burnout when it occurs.

The financial-services industry has made some progress in closing the gender and race gaps, but there is still a long way to go. As financial-services firms reimagine the future of the workplace, this moment calls for bold action to improve gender and racial diversity across the talent pipeline and create an inclusive culture where all women, and all employees, feel like they belong.

The authors gratefully acknowledge the partnership of LeanIn.Org and extend their thanks for its contribution to the thinking that appears in this report. The authors also wish to acknowledge the contributions of Kristen Cooper, Worth Gentry, and Tijana Trkulja to this article.

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Inference and Representation: A Study in Modeling Science

Mauricio Suárez, Inference and Representation: A Study in Modeling Science , University of Chicago Press, 2024, 328pp., $35.00 (pbk), ISBN 9780226830049.

Reviewed by Robert Hudson, University of Saskatchewan

What is involved when someone, such as a scientist, uses a model to represent the world? According to Mauricio Suárez, we can examine this question in one of two ways: in terms of an analytic inquiry that answers a ‘constitutional’ question, or in terms of a practical inquiry that answers a ‘means’ question (84–89).

Traditionally, representation is understood constitutionally, “identifying [representation] entirely with the set of facts about the properties of the relata” (7). Here, the relata are the source of representation, “the object doing the representational work”, and the target of representation, “the object getting represented” (6). The traditional approach, which Suárez labels ‘reductive naturalism’, provides a metaphysical analysis of the representational relation, one that “[avoids] any reference to human values [and] . . . the interests, desires, and purposes of the inquirers” (7).

Suárez’s recommended approach is to examine representation in terms of its means, “focusing instead on the very diverse range of models and modeling techniques employed in the sciences”, while paying close attention to “the purposes of those who use and develop the representations” (86). This change of focus reflects, on Suárez’s view, a disciplinary shift in the philosophy of science where analytic inquiries are replaced with “an attempt to understand modeling practices”, a shift indicated by “the intense intention that philosophers have paid to scientific models and modeling practice in the last decades” (85).

Where does this refocusing on matters of scientific practice, and away from questions of metaphysical analysis, lead us? Suárez starts in Chapter 2 by examining the reflections on scientific practice of a unique set of 19th century physicists, Herman von Helmholtz, Heinrich Hertz, James Clerk Maxwell, and Ludwig Boltzmann, and identifies in these reflections an expression of what Suárez calls the ‘modeling attitude’, “a rather loose set of normative commitments . . . that bounds and informs [this] practice within recognized parameters” (44). He continues in Chapter 3 by reviewing a further unique set of contemporary modeling practices rooted in 19th century science, “the engineering model of the 1890 Forth Rail Bridge, the billiard ball model of gases, and stellar structure models in astrophysics” (79). For those familiar with Suárez’s previous work, chapters 2 and 3 constitute new material (xi).

In comparison, chapters 4 to 7 are reworkings of previously published material, developing and arguing for the details of Suárez’s inferential, deflationist theory of model representation, now ‘inspired’ by the 19th century modeling attitude and employing the three case studies as ‘benchmarks’ (84). Chapter 8 presents novel material in support of a deflationist conception. The classic source of philosophical discussion of representation occurs in the philosophy of art and Suárez finds that his representational deflationism “exhibits a notable fit” (223) with Richard Wollheim’s view of the experience of ‘seeing-in’. Chapter 9 concludes the book with original assessments of familiar debates in the philosophy of science. Concerning the realism/anti-realism debate, deflationism resuscitates the tenability of Ian Hacking’s entity realism, Bas van Fraassen’s constructive empiricism, and Arthur Fine’s natural ontological attitude. Further, the turn to emphasizing the role of social practice, characteristic of Suárez’s deflationism, enhances both Philip Kitcher’s ‘real realism’ and Helen Longino’s social epistemology. Finally, the absence of a facticity requirement on successful modeling, as Suárez sees it, provides support for Henk de Regt’s account of scientific understanding.

Suárez’s book rewards the attentive reader with its thorough detail, meticulous argumentation, and scholarly richness. Whether it provides a defensible view of scientific representation turns on whether we describe the representational relation analytically, in terms of the ‘substance’ of this relation (as with reductive naturalism, a substance devoid of “pragmatic elements”; see 91), or practically, deflating this relation and focusing instead on the use of representational sources in generating corroborated inferences about their targets. Classic substantivism views representation in terms of the similarity of a target and a source, or their isomorphism (or weaker, their homomorphism, or other morphism). A recognized problem with substantivism is the phenomenon of misrepresentation (113): where there is no target, or where a target lacks relevant properties, there can be no representation on the substance view as there are no grounds for similarity or isomorphism, and so no misrepresentation.

In contrast, Suárez’s theory of model representation has two components. First, a source represents a target only if the ‘representational force’ of the source “points toward” (9) the target (166). The notion of representational force is understood weakly: a source is directed to the target, and nothing else. The significance of representational force is that this direction is determined practically, in accordance with intended social use (119). This is the deflationary aspect of Suárez’s conception. There’s nothing about the source or the target, in themselves, that necessitates representational force. It follows that anything can represent anything else, the relevant social practice willing (47, 85, 189).

Secondly, on Suárez’s view, a source represents a target only if a source has a “specific inferential capacity” toward a target (166). Inferential capacity comes in two forms. First, there are vertical rules of inference, rules that “apply to the internal workings of the sources considered as self-standing objects” (184). Drawing from Heinrich Hertz, models ( Bilder , for Hertz; 38–39) exhibit ‘conformity’. They possess an internal, “inferential structure” (39) that grants them “a life of their own” (184), one that is “thoroughly social” (227). On the other hand, to serve the purpose of representing a target, a source’s inferential capacity involves horizontal rules of inference “essentially linked to [this source’s social] purposes in surrogative reasoning”, here reasoning about a target to the point of making licensed predictions about the target’s behaviour.

The implications of Suárez’s theory of representation are many. Chapter 7 illustrates the valuable use of surrogative reasoning in Suárez’s chosen case studies, cited above. Also, the application of Suárez’s theory to the philosophy of art opens “a Pandora's box of new questions” as soon as one draws licensed inferences from artworks in a “cultural and political context” (222). Further, Suárez’s deflationism breathes new life into van Fraassen’s constructive empiricism (242–243), now freed of cumbersome metaphysics.

Overall, one would have expected Suárez, given his retrospective position, to have spent more time reviewing published objections to his view. He orients his deflationism in the context of R.I.G. Hughes’ (1997) DDI account (141), arguing that his notion of representational force (“denotative function”) is an improvement on what Hughes calls ‘denotation’ (147–151). On the other hand, Roman Frigg and James Nguyen’s recent DEKI account is ignored, along with its critique of Suárez’s inferentialism. For example, Nguyen and Frigg (2022) object that Suárez fails to satisfactorily answer the “Semantic question: in virtue of what does a model represent its target” (7). Typically, we have an idea about the ‘meaning’ of a model prior to saying what inferences a model prescribes. Inferentialism works the other way. Since representational force, as noted above, is utterly deflated—anything can represent anything else—inferential capacity is the primary driver of meaning. With only inferences at hand, “there is no substantial analysis to be given about scientific representation” (Nguyen and Frigg 2022, 45), about what models represent or mean.

In specifying what it is in virtue of which a model represents a target, we need to say something about what a model is (about what Nguyen and Frigg call a “model object”, 66). This is not to ask for the necessary or sufficient conditions for being a model (its ‘constitution’). It is to ask, in a case where a model represents target, what specifically the model is—what thing it is—that is doing the targeting, just as when someone drives a car we ask, specifically, who is doing the driving, and not for the necessary or sufficient conditions for being a driver. Take, then, Suárez’s case of the Forth Rail Bridge. The (scale) model in this case is a set of engineering blueprints, some of which Suárez reproduces (62–63). These blueprints are the source, the model, and the target is the physical bridge. This is almost right. I have another copy of Suárez’s book, with the same blueprints. I don’t, therefore, have two distinct models of the bridge. It’s one model reproduced twice, reproduced many times in all the copies of the book, reproduced anthropomorphically as on the cover of Suárez’s book, which is itself reproduced multiple times with multiple copies of the book, and so on. So, in specifying what model it is that targets the physical Forth Rail Bridge, we need to look beyond the blueprints. This has nothing to do with the abstractness of the blueprints as a representation of the bridge. The anthropomorphic model is concrete, and with it, too, we need to look beyond the people in the depiction, to the same model that is at issue with the blueprints.

These comments are not original. They speak to the need for caution in talking in a facile way about models, or model objects. Nguyen and Frigg are aware of this need and highlight the relevant ontological issues. One can look at models as (set-theoretic) structures or as fictional entities (2022, 66). Suárez focuses on disputing the structure approach (138). For example, the Forth Rail Bridge blueprints are not set-theoretic. Their creator was not a modern logician. On the other hand, Suárez does not discuss a fictional approach. Arguably, the blueprints are not fictional since both they and the bridge are physically real. The question, for us, is whether Suárez’s deflationism handles this ontological quandary about models.

Consider again the question of the car and who the driver of the car is. A deflationist on this matter sidelines questions about the identity of this individual. Substantivist approaches, such as those based on similarity or isomorphism, encounter counterexamples since, analogously to Suárez’s arguments about models, potential car drivers need not be similar nor isomorphic to one another. The turn to a practical, or ‘means’ inquiry recommends that we look at the socially sanctioned practices of car drivers, without settling on the constitution of these drivers. For example, we might note that car drivers perform certain actions under certain circumstances, and different actions under different circumstances. A full description of these contextualized practices answers the question for a deflationist about who the driver is.

Is this a satisfactory answer to the analogous ontological question about drivers? Not if we think it matters who the driver is, leaving aside the question of their constitutional identity. At the traffic stop, a police officer will ask for the driver’s license and registration in order to pick out the relevant legal individual, not to define this person in terms of the necessary or sufficient conditions for being a driver. It’s a matter of ascribing responsibility for the driver's actions. A deflationist answer, substituting the legal individual with a set of actions practically distinguished by the interests of a community, is misleading since the same individual could perform a different set of actions, and a different individual could perform the same set of actions.

Consider now the Forth Rail Bridge. If one wants a reason for why the bridge has not toppled, one points to the relevant model. We access this model by viewing the blueprints. The blueprints aren’t the model since the blueprints are not responsible for why the bridge has not toppled. One can destroy all the blueprints and the bridge will still not topple. That the bridge has not toppled, or in more scientific cases, the success of one’s inferential practices, does not explain the lack of toppling or the bridge’s continued standing. These points are not distant from Suárez’s thinking. In discussing the Lotke-Volterra equations, Suárez notes that merely satisfying these equations is not enough to explain an observable phenomenon, such as the correlation between predator and prey numbers in the Adriatic Sea, since this correlation could be “entirely spurious or arbitrary” (114). Thus, the Lotke-Volterra theoretical model is more than just the equations and the inferential practices they prescribe. There is something in the world that corresponds to this model, something we have captured in our thinking, something ensuring that the model is not, as Suárez says, “predictively inane” (114). If the Lotke-Volterra model simply prescribes “a nonlinear pair of intermingled equations” and imposes “no requirements whatever on the nature of the objects involved as source or target or their relation” (172), there will be “no explanatory fact underlying the correlation” (114). To me, this sounds like an abandonment of inferentialism.

These critical points aside, Suárez’s book is a richly argued model of scholarship that sets the standard for future investigations into scientific representation.

Hughes, R.I.G. (1997), “Models and Representation,” Philosophy of Science 64: S325–S336.

Nguyen, J. and R. Frigg (2022), Scientific Representation . Cambridge University Press.

Who will win the 2024 election? What the polls say ahead of DNC

Since taking the reins last month as presumptive nominee of the Democratic party, Vice President Kamala Harris has seen a sharp rise in the polls over Biden’s performance.

The endgame of the presidential race is still months away and it’s too early to draw hard conclusions from current polling numbers — which are likely to shift and sway over the next three months.

But several recent nationwide polls show Harris with a slight lead over Republican nominee former President Donald Trump, even as the average among the critical battleground states remains tight.

Will Trump or Harris win?

A CBS News and YouGov poll of likely voters concluded on August 16 shows Kamala Harris polling at 49% nationally to Donald Trump’s 47%.

CBS’s polling also shows that the percentage of registered Democrats who say that they’ll vote in November is up 6% from a month ago, from 81% to 87%, while that same measure is down for Republicans, from 90% to 88%.

Among likely voters, CBS found that top issues influencing votes for president were the economy (83%), inflation (76%), the state of democracy (74%), crime (62%), gun policy (58%), the U.S.-Mexico border (56%) and abortion (51%).

There’s a relatively large gap between the two presidential candidates in terms of how familiar voters are with their platforms in the CBS poll. A full 86% of respondents said they knew what Trump stands for but only 64% said the same of Harris.

This could perhaps give Harris an opportunity to expand her appeal as she looks to further define her political persona and her policy platform under the spotlight of this week’s Democratic National Convention.

Trump is still in the lead among respondents who say that their main voting issues are the economy, inflation and border issues.

Republican vice-presidential nominee JD Vance cast spurious doubt on the reliability of polling broadly, telling Fox News that “The media uses fake polls to drive down Republican turnout and to create dissension and conflict with Republican voters.”

The Trump campaign has, however, plugged polling numbers before, when they were in his favor.

Emerson College shows Harris up, at 48% compared to Trump’s 44%.

An August 13 poll by The Economist has Harris at 46% and Trump at 44%.

A Washington Post /ABC News/Ipsos poll, also concluded August 13 shows Harris in the lead, 47% to 44%.

The New York Times ’ national polling average puts Harris ahead with 46% against Trump’s 45%.

A smaller number of polls still show Trump ahead—a poll from RMG Research and the Napolitan Institute shows Trump leading, 49% to 47% and another from J.L. Partners and Dailymail.com show him up 43% to 41%.

In a poll conducted August 9-12, Fox News had both Trump and Harris at 45%.

Who is winning on the state level?

The picture becomes more complicated when you start looking at individual states. Because of the electoral college, being ahead nationally doesn’t necessarily translate into taking office in January.

According to New York Times averages, Harris had pulled ahead of Trump in several important Rust Belt battleground states including Michigan (49-47%), Wisconsin (49-47%) and Pennsylvania (49-48%).

The Times average shows Trump holding his lead in certain Sun Belt states including Georgia, where he’s ahead 49% to 46% and in Arizona Trump and Harris both have 47%.

However, a Times/Siena poll from Thursday has Harris winning in Arizona, 47% to 43%, though it still shows Trump up in Nevada (46 to 44%) and in Georgia (47 to 44%.)

Emerson College shows Trump up very slightly in Pennsylvania, with both him and Harris rounded to 47%. Polls earlier this month from Franklin and Marshall College and Quinnipiac University, however, both show Harris up in Pennsylvania by 3 points, 46% to 43% and 48% to 45%, respectively.

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Enhancing gender data on UN Security Council representatives

The UN Dag Hammarskjöld Library has completed a notable project that enriches the data available on the historic gender ratio of UN Security Council representatives.

This initiative enables researchers, policymakers, and the public to gain insights into the evolving gender dynamics within the Council through a simple search in the UN Digital Library .

The project involved a meticulous review and update of individual name records for over 4,800 Security Council representatives from 1946 to the present.

The Library team ensured accuracy by checking for duplicates, distinguishing between individuals with similar names, and confirming state representation. Importantly, they added gender diacritics to the names, allowing users to effortlessly search and analyze the data based on gender.

One key outcome is the ability to track the historic gender balance among Security Council representatives. Delegates, UN staff, and researchers worldwide can now readily explore how gender representation has changed over time, identify trends, and analyze progress towards gender equality in global governance.

They can now easily determine the first woman Security Council President, which permanent member has contributed the most women to the Council, and more.

This enriched data opens up new avenues for research and policy discussions on the importance of gender diversity in international decision-making. It provides a valuable resource for further analysis.

Download the enhanced dataset from the UN Digital Library:

Access and utilize this dataset to gain deeper insights into the gender dynamics within the UN Security Council.

For questions or assistance, please contact the UN Library Team .

A day in the life of a Humanitarian Affairs Officer in CAR

“Our 'raison d’être' is to save and improve lives,” says Noelia Blascovich. “We must always remain humble, because it is not about us - it is about the people we serve.”

Help shape the future: Take the UN Library Global Survey

This is your opportunity to share your experiences and help shape the future of the services of the UN Dag Hammarskjöld Library in New York.

Annual report on the safety and security of humanitarian workers

As we marked World Humanitarian Day, the Secretary-General mourned the 219 United Nations and 172 humanitarian personnel who lost their lives while helping those in need.

DOCUMENTS AND PUBLICATIONS

• Africa Renewal
• e-Blue Book
• Delegates Handbook
• The Essential UN
• Journal of the United Nations
• Meetings Coverage and Press Releases
• Subscribe to documents
• UN Editorial Manual
• Yearbook of the United Nations

LIBRARIES AND ARCHIVES

• Audiovisual Library of International Law
• Diplomatic Pulse
• UN Archives and Records Management
• UN Audiovisual Library
• UN iLibrary
• United Nations Official Document System (ODS)
• New York Services & Resources (parking, medical, etc.)
• Protocol and Liaison Service
• UN News Outlets
• Duty Stations

SECURED CONTENT

• Secured sites - Who to contact
• gMeets - electronic meeting scheduling
• UN Telephone Directory
• Web creation and hosting