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Excel Chap 2 – Beyond the Basics

Absolute versus static references, understanding complex formulas, date & time functions, logical functions, more math functions, sorting and filtering, conditional formatting, bar & column charts, line charts.

Conditional Formatted sheet

Cell referencing is an extremely useful feature when formulas need to be copied across ranges in a worksheet. When creating formulas that contain references to cells or cell ranges, the default cell reference is considered to be a relative cell reference. When formulas with these type of cell references are copied to other cells the formulas will automatically change relative to the cells that they are copied to. However, there may be instances where it is necessary for Excel to keep the exact cell referenced in a formula when copying to other cells. A cell reference that does not change when copied is called an absolute cell reference (sometimes called a fixed cell reference). The indicator that a cell reference is absolute is the presence of a dollar sign symbol in front of both the column letter and row number, such as $A$3. To create an absolute cell reference, either type the dollar sign manually, or press the F4 after entering the cell reference. Repeatedly pressing the F4 key cycles the reference through the four different combinations of relative, absolute, and mixed cell references.

Mixed cell references are a combination of relative and absolute: either the column is relative and the row fixed (absolute), for example D$2, or the column is fixed and the row relative: $D2. Mixed cell references are rarely used, but they play a significant role when it is necessary to keep a single row or column unchanged while copying the formula. Mixed cell references are commonly used when creating a table of values, like a multiplication table or a mortgage rate table.

Relative Cell Reference

Formulas can be simple mathematical formulas or complicated formulas involving multiple mathematical operations, multiple cell ranges and nested functions. While it is a good idea to remember the order of operations rules, complex formulas can use parentheses to identify the arguments of functions and to override the order of operations. In mathematical operation formulas, operations within parentheses are performed before those outside of it. For example, in =A3+B3*C3, B3 is multiplied by C3 before A3 is added to the result, but in =(A3+B3)*C3, A3 and B3 are added together first, then the result is multiplied by C3.

Complex Formula

The TODAY and NOW functions are very similar since both return the current system date. However, the NOW function also returns the current system time. Many users format the results of the NOW function to only display the current system time. One characteristic of these functions versus the DATE function is that TODAY and NOW are volatile functions, so if the workbook is opened tomorrow, these functions will update automatically, whereas the DATE function will not change. These functions are for use within the grid of the worksheet, typically to calculate durations. There are separate Date and Time fields for use in worksheet headers and footers.

Many employers and educators are placing increasing emphasis on the value of critical thinking. Critical thinking skills are often associated with problem solving skills, empathy, and thinking and acting in purposeful ways by making fact-based decisions. Excel is a practical tool for collecting and analyzing data critically. Excel’s logical functions are especially useful for enabling critical thinking. However, before exploring the utilization of Excel’s logical functions, it is necessary to review the logical operators that are used to compare data between cells. The operators are often referred to as comparison operators. The six main logical operators are explained in the following graphic:

Comparison operators

These comparison operators can be used in Excel functions to compare all types of data, including dates, numbers, Boolean values (True or False, Yes or No), or text. All arguments must evaluate to the Boolean values of either True or False, or contain another, nested logical function.

The IF function is one of the most popular and useful functions in Excel. It can be used to make a decision based on a comparison. If the comparison is true, one value is displayed in the cell; if the comparison is false, a second value is displayed. The syntax of the IF function is: IF(logical_test, [value_if_true], [value_if_false]).

  • logical_test  – a value or logical expression that can be either TRUE or FALSE. Required.In this argument, you can specify a text value, date, number, or any comparison operator.
  • value_if_true  – the value to return when the logical test evaluates to TRUE, i.e. if the condition is met. Optional.
  • value_if_false – the value to be returned if the logical test evaluates to FALSE. Optional.

Simple IF

Instead of returning text strings, the IF formula can test the specified condition, perform a corresponding math operation and return a value based on the result. This is done by using arithmetic operators or other Excel functions in the value_if_true and /or value_if_false arguments. For example, =IF(C4>=D4, E4*.25, E4*10%). This formula is determining if the value in column C is greater than or equal to the value in column D. If the result of the comparison is true, then the value to be displayed should be the value in column E multiplied by .25 (25%). If the result of the comparison is false, then the value to be displayed should be the value in column E multiplied by 10% (.10).

Other popular Excel Logical functions include the AND , as well as the OR functions. These functions allow users to create multiple logical tests within a single IF function. These functions return either TRUE or FALSE results when their arguments are evaluated. The AND function only returns TRUE if every condition is met. However, the OR function returns TRUE if any condition is met. The syntax of both functions are the same: =AND(logical1, logical2, etc.) Examples of each function are illustrated in the screenshots below. The first illustration uses the AND function to determine if any of the people are eligible for the Inner Circle. They need to have a Customer Satisfaction Score of at least 4.0, and be a Vikings fan. The second example uses the OR function. The more lenient comparison operator yields more eligible people for the Inner Circle.

AND function

Practice 7: Expense Report

Expense Template

  • Date : 5/30/2019
  • Description : Travel to Minneapolis
  • Mileage : 205
  • Lodging : 150
  • In cell G9 enter the following complex formula using relative and absolute cell references: =C9+(D9*$C$6)+E9+F9   (are the parenthesis necessary?)
  • Format columns C, E, F and G as Currency format with two decimals.
  • Date : 5/31/2019
  • Description : Travel home
  • Use the fill handle to copy the formula in G9 to G10.
  • Insert a new row below the Mileage Rate row, and in B6 enter the label: Trip Duration. (bold the label)
  • In cell C6 enter a formula that subtracts A9 from A10. Change the format of cell C6 to General.
  • In cell B15 enter the label: Totals: (right-align & bold this cell).
  • Select cells C15:G15 and click the AutoSum button. Change the format of D15 to General.
  • Enter the label: Need Receipts? in cell B2. (bold the label)
  • In cell C2, enter the following logical function: =IF(F15>0,”Yes”,”No”)

Helga Expenses

Worksheets can have large amounts of data, and it can be overwhelming if it is not sorted correctly. Arranging data in a specified order is called sorting . Rows can be sorted in either ascending (low to high) or descending (high to low) order. Ascending order can also be considered alphabetic order if the data is text or chronological order if the data is dates or times.

Before data can be sorted, Excel needs to know the exact range of cells that is to be sorted. Excel will select areas of related data as long as th ere are no blank rows or columns in the data range. Blank rows and columns define the outer limits of the data range. To ensure that the correct data is selected, highlight the range before starting the sort.

As Excel determines the defined range of data to be sorted, Excel also determines if field names exist. Users should format the first row of the data range with unique formatting Often, just making the labels bold will help Excel identify the field names. Identifying the field names will prevent Excel from including these fields in the records to be sorted. The field names become the sort keys needed for multiple column sorts. In the image below, the possible sort keys are: Cruise Date, Accommodation Category, Rooms Available, Rooms Rented, Rate, Revenue and Shortfall.

Sort Data Range

To remove a single filter, click the filter icon in the row header and choose Clear Filter from…. To clear all filters quickly, choose the Clear button from the Data tab on the ribbon or to remove filtering functionality, re-click the Filter icon from the Sort & Filter group. For more advanced users there are many more ways to utilize filters in Excel, such as Custom Filters and Advanced Filters. Nonetheless, a lot can be accomplished with the basic AutoFilter feature.

Conditional Formatting icon

The icon sets work great when color is not effective, such as when printing to black & white laser printers. Icons are even more noticeable than colors because of their unique look and sparing use.  Icon sets will help visually represent the data with directional arrows, shapes, indicators, ratings, and other objects. For icons in sets of three, Excel will assign icons by dividing values into thirds – the first icon is assigned to the top one third of values, the second icon is assigned to the second third of values, and the third icon is assigned to the lowest one third of values. The values are adjusted for four and five-icon sets. Conditional formatting’s flexibility is extensive, but perhaps even more impressive is that, like formulas, conditional formatting rules are volatile. As the data changes, the conditional formatting dynamically adjusts to evaluate the new data against the existing conditional rules.

With Excel, users can organize data so that it has context and meaning. The output of Excel manipulation can take the shape of either a table or chart. When deciding to use a chart or a table to communicate the data-driven message, it is wise to always ask how the information will be used, and who is the audience? People interact very differently with these two types of visuals. Tables , which display data in a columnar layout, are meant to be read. Therefore tables are ideal when the data requires more specific analysis. Tables offer preciseness, letting users dive deeper to crunch the numbers and examine exact values, instead of focusing on approximations or visualizations.

A chart is a visual representation of a range of related worksheet data. A chart can illustrate a large amount of numerical data quickly and in an easy-to-understand fashion. Charts are particularly useful for simplifying complex sets of data to expose  the shape of the data – numerical patterns, trends, and other significant activity. What charts lack in terms of precision they overcome with broader insight and quicker comprehension.

brain theory

Learning how to work with charts means not only knowing how to create them but also realizing that different types of chart and layouts can reveal and emphasize different knowledge. Like a picture, a chart can be worth a thousand words. It all depends on how well the chart is designed and developed. A well constructed chart will provide context and clarity for data analysis and story telling. The first step to creating useful charts it to organize and precisely select the data that should be charted. This includes the cells that contain both the data and the label headings.

Each chart type conveys information in different ways. Pie charts , for example, are best for charting data that is a percentage of a whole. For example, what percentage of your monthly income is spent on transportation? Charts contain different objects for each chart type. Objects in a pie chart include:

  • Chart title – describes what is charted. The label heading of the data series is used by default, but this can be edited.
  • Legend – an index of information that corresponds to the category labels.
  • Data labels – identify each value in the data series.
  • Plot area – the part of the chart that displays data graphically.
  • Chart area – the entire chart and all of its elements.

Pie chart annotated

Which pie chart looks better? Generally, removing the legend through use of data labels is considered a preferable design strategy. Alas, there are even more ways to customize a pie chart that is beyond the scope of this text! Additional functionality includes creating 3-D pie charts, exploding slices, rotating, sorting, adding different fill designs, and much more!

Bar charts are practical for comparing the differences between values with horizontal bars. The lengths of the bars are proportional to the size of the data category they represent. A vertical bar chart is referred to as a column chart, and they are basically the same – just 90° apart. Unlike a pie chart, a bar chart can include several series of data. Bar charts are simple, easy and flexible, and thanks to the horizontal layout, bar charts can accommodate longer category names. Bar (and column) charts contain the following objects:

  • Chart title – describes what is charted.
  • Plot area – the region within the horizontal and vertical axes.
  • Axes titles (horizontal, vertical)- describe the data.
  • Legend – an index of information that corresponds to the series names.
  • Data labels – identify each value in a data series.
  • Value axis (y-axis) – contains values. Horizontal axis on bar charts and vertical axis on column charts.
  • Category axis (x-axis) – contains the category labels. Horizontal axis on column charts and vertical axis on bar charts.
  • Gridlines – mark the intervals on an axis.

bar chart annotated

While the data and chart above only displays one data series, most bar and column charts tend to display multiple data series to compare and contrast one set of data against another. The chart below adds a second data series in column C, and changes the chart type to a column chart. The two different data series are illustrated with different color data points. Also, note how the axes change directions! The value axis maximum, major and minor units were also modified to different numerical values.

Multiseries column chart

In a Line Chart, the vertical axis (Y-axis) always displays numeric values and the horizontal axis (X-axis) displays time or other categories. Time intervals can be measured in years, months, days, or hours.

Microsoft Excel

In the 2-D line chart illustrated above, two sets of data series are plotted for fifteen days. The Skinny Mints cookies are identified by the red line, and the orange line plots the Chocolate/Peanut Butter cookies. Each date is a data point. Additional data series can be added by expanding the data source range. Line charts provide an easy way to track historical data. In many cases, the way the data is trending makes it easy to predict the results of data in future periods.

Excel offers numerous other charts that might better help illustrate the story behind the data, however all charts must address the challenge of sharing or outputting the graphic(s) to their target audience(s). Here are a few printing issues to consider:

Excel Print Preview Line Chart

  • Chart colors that are not compatible with black and white printers. A lot of office printers are black and white laser printers due to their low-cost to operate at high volumes. A color laser printer may be a worthy investment for common chart printing. If a black and white printer is all that is available, it may be necessary to change the colors to patterns or contrasting shades of grey.
  • Not enough or too much information. Reads of the chart must be able to comprehend the message the chart is attempting to convey. This might require adding context, such as titles, data labels, and text-box callouts. Conversely, a chart can have too much information that the chart is cluttered and unreadable. In this case, summarizing the data my be prudent, or even re-selecting a different source data range. A chart can also be unreadable due to poor design considerations like wrong fonts and font sizes, as well as distracting colors and object sizes.
  • Excel charts are volatile and will change as often as the source data is changed. If a static copy of a chart is needed, consider saving the chart as a picture. This can be accomplished through using the copy and paste special commands. Using Paste Special will allow a chart to pasted in either PNG, JPEG, GIF or other formats. Alternatively, Excel files can be saved as PDF files for inserting in other electronic documents/files.

Practice 8: Weather Report

  • Open the data file The Weather Report.xlsx or create a new sheet from the illustration at right.
  • Add conditional formatting to all cells in B6:E17 so that any cell is at least 90° with red fill cell formatting, or below 32° in light blue fill.
  • Use the Internet to research average monthly high temps for Fort Myers, FL. Enter a label and the temps in column E. The conditional formatting should dynamically format the cells.
  • Create a 2-D bar chart of Anchorage and Mesa temps for all twelve months.
  • Move the bar chart to its own chart sheet.
  • Return to the original source data sheet and create an embedded 2-D line chart with markers for all four cities for all twelve months. Change the chart title to Average Month High Temps. Move the chart slightly so the top-left edge is in cell F6.

Weather Report Line Chart

  • Save the file as The Weather Report2.xlsx to your hard drive.

Business Computers 365 Copyright © 2019 by Marcus Lacher is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License , except where otherwise noted.

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Pursuing Truth: A Guide to Critical Thinking

Chapter 2 arguments.

The fundamental tool of the critical thinker is the argument. For a good example of what we are not talking about, consider a bit from a famous sketch by Monty Python’s Flying Circus : 3

2.1 Identifying Arguments

People often use “argument” to refer to a dispute or quarrel between people. In critical thinking, an argument is defined as

A set of statements, one of which is the conclusion and the others are the premises.

There are three important things to remember here:

  • Arguments contain statements.
  • They have a conclusion.
  • They have at least one premise

Arguments contain statements, or declarative sentences. Statements, unlike questions or commands, have a truth value. Statements assert that the world is a particular way; questions do not. For example, if someone asked you what you did after dinner yesterday evening, you wouldn’t accuse them of lying. When the world is the way that the statement says that it is, we say that the statement is true. If the statement is not true, it is false.

One of the statements in the argument is called the conclusion. The conclusion is the statement that is intended to be proved. Consider the following argument:

Calculus II will be no harder than Calculus I. Susan did well in Calculus I. So, Susan should do well in Calculus II.

Here the conclusion is that Susan should do well in Calculus II. The other two sentences are premises. Premises are the reasons offered for believing that the conclusion is true.

2.1.1 Standard Form

Now, to make the argument easier to evaluate, we will put it into what is called “standard form.” To put an argument in standard form, write each premise on a separate, numbered line. Draw a line underneath the last premise, the write the conclusion underneath the line.

  • Calculus II will be no harder than Calculus I.
  • Susan did well in Calculus I.
  • Susan should do well in Calculus II.

Now that we have the argument in standard form, we can talk about premise 1, premise 2, and all clearly be referring to the same thing.

2.1.2 Indicator Words

Unfortunately, when people present arguments, they rarely put them in standard form. So, we have to decide which statement is intended to be the conclusion, and which are the premises. Don’t make the mistake of assuming that the conclusion comes at the end. The conclusion is often at the beginning of the passage, but could even be in the middle. A better way to identify premises and conclusions is to look for indicator words. Indicator words are words that signal that statement following the indicator is a premise or conclusion. The example above used a common indicator word for a conclusion, ‘so.’ The other common conclusion indicator, as you can probably guess, is ‘therefore.’ This table lists the indicator words you might encounter.

Therefore Since
So Because
Thus For
Hence Is implied by
Consequently For the reason that
Implies that
It follows that

Each argument will likely use only one indicator word or phrase. When the conlusion is at the end, it will generally be preceded by a conclusion indicator. Everything else, then, is a premise. When the conclusion comes at the beginning, the next sentence will usually be introduced by a premise indicator. All of the following sentences will also be premises.

For example, here’s our previous argument rewritten to use a premise indicator:

Susan should do well in Calculus II, because Calculus II will be no harder than Calculus I, and Susan did well in Calculus I.

Sometimes, an argument will contain no indicator words at all. In that case, the best thing to do is to determine which of the premises would logically follow from the others. If there is one, then it is the conclusion. Here is an example:

Spot is a mammal. All dogs are mammals, and Spot is a dog.

The first sentence logically follows from the others, so it is the conclusion. When using this method, we are forced to assume that the person giving the argument is rational and logical, which might not be true.

2.1.3 Non-Arguments

One thing that complicates our task of identifying arguments is that there are many passages that, although they look like arguments, are not arguments. The most common types are:

  • Explanations
  • Mere asssertions
  • Conditional statements
  • Loosely connected statements

Explanations can be tricky, because they often use one of our indicator words. Consider this passage:

Abraham Lincoln died because he was shot.

If this were an argument, then the conclusion would be that Abraham Lincoln died, since the other statement is introduced by a premise indicator. If this is an argument, though, it’s a strange one. Do you really think that someone would be trying to prove that Abraham Lincoln died? Surely everyone knows that he is dead. On the other hand, there might be people who don’t know how he died. This passage does not attempt to prove that something is true, but instead attempts to explain why it is true. To determine if a passage is an explanation or an argument, first find the statement that looks like the conclusion. Next, ask yourself if everyone likely already believes that statement to be true. If the answer to that question is yes, then the passage is an explanation.

Mere assertions are obviously not arguments. If a professor tells you simply that you will not get an A in her course this semester, she has not given you an argument. This is because she hasn’t given you any reasons to believe that the statement is true. If there are no premises, then there is no argument.

Conditional statements are sentences that have the form “If…, then….” A conditional statement asserts that if something is true, then something else would be true also. For example, imagine you are told, “If you have the winning lottery ticket, then you will win ten million dollars.” What is being claimed to be true, that you have the winning lottery ticket, or that you will win ten million dollars? Neither. The only thing claimed is the entire conditional. Conditionals can be premises, and they can be conclusions. They can be parts of arguments, but that cannot, on their own, be arguments themselves.

Finally, consider this passage:

I woke up this morning, then took a shower and got dressed. After breakfast, I worked on chapter 2 of the critical thinking text. I then took a break and drank some more coffee….

This might be a description of my day, but it’s not an argument. There’s nothing in the passage that plays the role of a premise or a conclusion. The passage doesn’t attempt to prove anything. Remember that arguments need a conclusion, there must be something that is the statement to be proved. Lacking that, it simply isn’t an argument, no matter how much it looks like one.

2.2 Evaluating Arguments

The first step in evaluating an argument is to determine what kind of argument it is. We initially categorize arguments as either deductive or inductive, defined roughly in terms of their goals. In deductive arguments, the truth of the premises is intended to absolutely establish the truth of the conclusion. For inductive arguments, the truth of the premises is only intended to establish the probable truth of the conclusion. We’ll focus on deductive arguments first, then examine inductive arguments in later chapters.

Once we have established that an argument is deductive, we then ask if it is valid. To say that an argument is valid is to claim that there is a very special logical relationship between the premises and the conclusion, such that if the premises are true, then the conclusion must also be true. Another way to state this is

An argument is valid if and only if it is impossible for the premises to be true and the conclusion false.

An argument is invalid if and only if it is not valid.

Note that claiming that an argument is valid is not the same as claiming that it has a true conclusion, nor is it to claim that the argument has true premises. Claiming that an argument is valid is claiming nothing more that the premises, if they were true , would be enough to make the conclusion true. For example, is the following argument valid or not?

  • If pigs fly, then an increase in the minimum wage will be approved next term.
  • An increase in the minimum wage will be approved next term.

The argument is indeed valid. If the two premises were true, then the conclusion would have to be true also. What about this argument?

  • All dogs are mammals
  • Spot is a mammal.
  • Spot is a dog.

In this case, both of the premises are true and the conclusion is true. The question to ask, though, is whether the premises absolutely guarantee that the conclusion is true. The answer here is no. The two premises could be true and the conclusion false if Spot were a cat, whale, etc.

Neither of these arguments are good. The second fails because it is invalid. The two premises don’t prove that the conclusion is true. The first argument is valid, however. So, the premises would prove that the conclusion is true, if those premises were themselves true. Unfortunately, (or fortunately, I guess, considering what would be dropping from the sky) pigs don’t fly.

These examples give us two important ways that deductive arguments can fail. The can fail because they are invalid, or because they have at least one false premise. Of course, these are not mutually exclusive, an argument can be both invalid and have a false premise.

If the argument is valid, and has all true premises, then it is a sound argument. Sound arguments always have true conclusions.

A deductively valid argument with all true premises.

Inductive arguments are never valid, since the premises only establish the probable truth of the conclusion. So, we evaluate inductive arguments according to their strength. A strong inductive argument is one in which the truth of the premises really do make the conclusion probably true. An argument is weak if the truth of the premises fail to establish the probable truth of the conclusion.

There is a significant difference between valid/invalid and strong/weak. If an argument is not valid, then it is invalid. The two categories are mutually exclusive and exhaustive. There can be no such thing as an argument being more valid than another valid argument. Validity is all or nothing. Inductive strength, however, is on a continuum. A strong inductive argument can be made stronger with the addition of another premise. More evidence can raise the probability of the conclusion. A valid argument cannot be made more valid with an additional premise. Why not? If the argument is valid, then the premises were enough to absolutely guarantee the truth of the conclusion. Adding another premise won’t give any more guarantee of truth than was already there. If it could, then the guarantee wasn’t absolute before, and the original argument wasn’t valid in the first place.

2.3 Counterexamples

One way to prove an argument to be invalid is to use a counterexample. A counterexample is a consistent story in which the premises are true and the conclusion false. Consider the argument above:

By pointing out that Spot could have been a cat, I have told a story in which the premises are true, but the conclusion is false.

Here’s another one:

  • If it is raining, then the sidewalks are wet.
  • The sidewalks are wet.
  • It is raining.

The sprinklers might have been on. If so, then the sidewalks would be wet, even if it weren’t raining.

Counterexamples can be very useful for demonstrating invalidity. Keep in mind, though, that validity can never be proved with the counterexample method. If the argument is valid, then it will be impossible to give a counterexample to it. If you can’t come up with a counterexample, however, that does not prove the argument to be valid. It may only mean that you’re not creative enough.

  • An argument is a set of statements; one is the conclusion, the rest are premises.
  • The conclusion is the statement that the argument is trying to prove.
  • The premises are the reasons offered for believing the conclusion to be true.
  • Explanations, conditional sentences, and mere assertions are not arguments.
  • Deductive reasoning attempts to absolutely guarantee the truth of the conclusion.
  • Inductive reasoning attempts to show that the conclusion is probably true.
  • In a valid argument, it is impossible for the premises to be true and the conclusion false.
  • In an invalid argument, it is possible for the premises to be true and the conclusion false.
  • A sound argument is valid and has all true premises.
  • An inductively strong argument is one in which the truth of the premises makes the the truth of the conclusion probable.
  • An inductively weak argument is one in which the truth of the premises do not make the conclusion probably true.
  • A counterexample is a consistent story in which the premises of an argument are true and the conclusion is false. Counterexamples can be used to prove that arguments are deductively invalid.

( Cleese and Chapman 1980 ) . ↩︎

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  1. Organizing Critical Thinking with Excel

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  1. SIA Computer Excel Chapter 2 Modified Critical Thinking

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  3. Excel Chapter 2: End-of-Chapter Quiz Flashcards

    A statistical function that counts the number of cells within a range that meet the given condition and which has two arguments- the range of cells to check and the criteria. Logical test. Any value or expression that can be evaluated as being true or false. IF function. A function that uses a logical test to check whether a condition is met ...

  4. Excel Chapter 2

    Excel is a practical tool for collecting and analyzing data critically. Excel's logical functions are especially useful for enabling critical thinking. However, before exploring the utilization of Excel's logical functions, it is necessary to review the logical operators that are used to compare data between cells.

  5. PDF Module 3: Excel and Critical Thinking

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  7. Excel Templates

    Click the links below to access the Excel Templates available for this chapter. Excel Template - Problem 4-8 (202.0K) Excel Template - Alternative Problem 4-2 (203.0K) Excel Template - Critical Thinking Case CP4-10 (215.0K) To learn more about the book this website supports, please visit its Information Center .

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  18. Excel Chapter 2 Study Guide Flashcards

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