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Mean Median Mode Range Worksheets and Help

Welcome to the Math Salamanders Mean Median Mode Range Worksheets. Here you will find a wide range of free printable Worksheets, which will help your child learn how to find the mean, median, mode and range of a set of data points.

These worksheets are aimed at students in 5th and 6th grade.

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Mean Median Mode Range Worksheets

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What is the Mean?

The mean is the average of a set of numbers.

It is found by adding up the set of numbers and then dividing the total by the number of data points in the set.

How to find the mean

Step 1) Add up all the numbers in the set.

Step 2) Divide the total by the total number of data points in the set.

Example 1) Find the mean of 5, 7, 8 and 4

Step 1) Add up the numbers to give a total of 5+7+8+4=24

Step 2) Divide the total by the number of data points. 24 ÷ 4 = 6

Answer: the mean is 6.

Example 2) Find the mean of 8, 2, 5, 7 and 13

Step 1) Add up the numbers to give a total of 8+2+5+7+13=35

Step 2) Divide by the number of data points. 35 ÷ 5 = 7

Answer: the mean is 7.

What is the Median?

The median is the midpoint (or middle value) of a set of numbers.

It is found by ordering the set of numbers and then finding the middle value in the set.

How to find the median

Step 1) Order the numbers in the set from smallest to largest.

Step 2) Find the middle number.

- If there is an odd number of values in the set, then the median is the middle value.

- If there is an even number of values in the set, then the median is the average of the two middle values.

Example 1) Find the median of 5, 7, 8, 2 and 4

Step 1) Put the numbers in order: 2, 4, 5, 7, 8

Step 2) There is an odd number of values in the set so the median is the middle value which is 5.

Answer: the median is 5.

Example 2) Find the median of 23, 27, 16, 31

Step 1) Put the numbers in order: 16, 23, 27, 31

Step 2) There is an even number of values in the set, so the median is the average of the middle two values.

(23+27) ÷ 2 = 25

Answer: the mean is 25

Example 3) Find the median of 7, -4, 9, -7, -2, 5

Step 1) Order the numbers: -7, -4, -2, 5, 7, 9

To get the average, simply add the two values together and divide by 2:

(-2 + 5) ÷ 2 = 1.5

Answer: the mean is 1.5

What is the Mode?

The mode is the most common (or the data point that appears most often) in a set of data.

It can be found by putting the data into an ordered list and seeing which data point occurs most often.

How to find the mode

Step 1) Put the data into an ordered list.

Step 2) Check that you have got the same number of data points.

Step 3) The mode is the data point which is the most common.

Finding the Mode Examples

Example 1) Find the mode of 3, 6, 4, 3, 2, 4, 7, 8, 6, 3, 9

This gives us: 2, 3, 3, 3, 4, 4, 6, 6, 7, 8, 9

Step 2) Check the number of data points in both lists is the same.

Both lists have 11 data points.

Step 3) The mode is the number which occurs most often.

Answer: the mode is 3.

Example 2) Find the mode of 0.6, 0.3, 0.4, 0.2, 0.4, 0.7, 0.6, 0.1, 0.4, 0.9

This gives us: 0.1, 0.2, 0.3, 0.4, 0.4, 0.4, 0.6, 0.6, 0.7, 0.9

Both lists have 10 data points.

Answer: the mode is 0.4.

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What is the Range?

The range is the gap between the smallest and largest data point.

It is found by putting the data into an ordered list and find the difference between the largest and smallest amount.

How to find the range

Step 3) The range is the difference between the largest and smallest data point.

To find the range simply subtract the smallest number from the largest number.

Finding the Range Examples

Example 1) Find the range of 14, 21, 9, 32, 27, 15, 12, 30

This gives us: 9, 12, 14, 15, 21, 27, 30, 32

Both lists have 8 data points.

Step 3) The range is the difference or gap between the largest and smallest numbers.

Answer: the range is 32-9=23.

Example 2) Find the range of 6, 2, -7, 2, -5, 11, 3, -4, 0, 9

This gives us: -7, -5, -4, 0, 2, 2, 3, 6, 9, 11

Answer: the range is 11-(-7)=18.

These printable mean median mode range worksheets have been carefully graded to ensure a progression in the level of difficulty.

Sheets 1, 2 and 3 are designed for 5th graders involve ordering and calculating using positive integers and decimals.

Sheets 4, 5 and 6 are designed for 6th graders and involve ordering and calculating with positive and negative numbers and decimals.

The first sheet involve finding the mean, median, mode and range of some positive whole numbers.

The 2nd sheet involves the use of decimals to 1dp.

The 3rd sheet is similar to the 2nd sheet but has many more data points.

The 4th sheet involves decimals and negative numbers.

The 5th and 6th sheets are similar to the 4th sheets but with increased number of data points.

• Mean Median Mode and Range Sheet 1
• PDF version
• Median Mean Mode and Range Sheet 2
• Median Mean Mode and Range Sheet 3
• Median Mean Mode and Range Sheet 4
• Median Mean Mode and Range Sheet 5
• Median Mean Mode and Range Sheet 6

Mean Median Mode Range Problems

These printable mean median mode range problem sheets will help your child to use and apply their skills to solve problems.

The first problem sheet is more suitable for 5th grade and the second sheet is aimed at 6th graders.

• Median Mean Mode and Range Problems 1
• Median Mean Mode and Range Problems 2

Mean Median Mode Range Walkthrough Video

This short video walkthrough shows the problems from our Median Mean Mode and Range Problems Sheet 2 being solved and has been produced by the West Explains Best math channel.

If you would like some support in solving the problems on these sheets, check out the video!

More Recommended Math Worksheets

Take a look at some more of our worksheets similar to these.

• Mean Worksheets

The sheets in this section will help you to find the mean of a range of numbers, including negative numbers and decimals.

There are a range of sheets involving finding the mean, and also finding a missing data point when the mean is given.

• Median Worksheets

The sheets in this section will help you to find the median of a range of numbers, including negative numbers and decimals.

On some of the easier sheets, only odd numbers of data points have been used.

On the harder sheets, both odd and even numbers of data points have been included.

• Mode and Range Worksheets

The sheets in this section will help you to find the mode and range of a set of numbers, including negative numbers and decimals.

There are easier sheets involving fewer data points, and harder ones with more data points.

The sheets in this section will help you to solve problems involving bar graphs and picture graphs.

There are a range of sheet involving reading and interpreting graphs as well as drawing your own graphs.

• Box Plot Worksheets

Here are our selection of box plot worksheets to help you practice creating and interpreting box plots.

Mean, Median, Mode and Range Online Quiz

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This quick quiz tests your knowledge and skill at finding and using the mean, median, mode and range of a set of data.

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Central Tendency Worksheets: Mean, Median, Mode and Range

Mean, median, mode and range worksheets contain printable practice pages to determine the mean, median, mode, range, lower quartile and upper quartile for the given set of data. The pdf exercises are curated for students of grade 3 through grade 8. Interesting word problems are included in each section. Sample some of these worksheets for free!

Finding Average

Average or mean worksheets have plentiful exercises to find the average of numbers, numbers with practical units and decimals.

(49 Worksheets)

Finding Range

Identify the maximum and minimum values to find the range of the given data. Word problems are included for practice.

• Download the set

Finding Median

In these worksheets, 3rd grade and 4th grade children identify the median (middle value) of the represented data. Two word problems included.

Finding Quartiles

Determine the first (lower) quartile, second (median) quartile and the third (upper) quartile of the given data. One word problem included in each pdf worksheet for 5th grade and 6th grade students.

Mean, Median, Mode and Range: Level 1

These printable central tendency worksheets contain a mixed review of mean, median, mode and range concepts. Around 8 data are used in level 1.

Mean, Median, Mode and Range: Level 2

Find the mean, median, mode and range of each set of data. Each sheet has six problems with around 15 data.

Word Problems: Level 1

This exclusive section has five word problems to find the mean, median, mode and range of the given data.

Word Problems: Level 2

A variety of informative data are included as word problems in these central tendency worksheet pdfs requires 7th grade and 8th grade students to determine the values of mean, median, mode and range.

Related Worksheets

» Line Plot

» Mean Absolute Deviation

» Stem and Leaf Plot

» Box and Whisker Plot

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Statistics and probability

Course: statistics and probability   >   unit 3.

• Statistics intro: Mean, median, & mode
• Mean, median, & mode example

Mean, median, and mode

Calculating the mean.

• Calculating the median
• Choosing the "best" measure of center

Mean, median, and mode review

Practice problems.

• Your answer should be
• an integer, like 6 ‍  
• a simplified proper fraction, like 3 / 5 ‍  
• a simplified improper fraction, like 7 / 4 ‍  
• a mixed number, like 1   3 / 4 ‍  
• an exact decimal, like 0.75 ‍  
• a multiple of pi, like 12   pi ‍   or 2 / 3   pi ‍  

Finding the median

• Arrange the data points from smallest to largest.
• If the number of data points is odd, the median is the middle data point in the list.
• If the number of data points is even, the median is the average of the two middle data points in the list.

Finding the mode

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Mean, Median, Mode, and Range

Mean, median, and mode are three kinds of "averages". There are many "averages" in statistics, but these are, I think, the three most common, and are certainly the three you are most likely to encounter in your pre-statistics courses, if the topic comes up at all.

Why do we need different kinds of averages?

The average that we're used to is found by adding all the values in a data set, and then dividing the sum by the number of values in that data set; but this average might be misleading.

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Median, Mode, and Range

A typical example would be the case where nearly every person in a given population lives on about two dollars a day, but there is a small elite with incomes in the millions. The numerical average can mislead by suggesting that the average (in this case, we mean "typical") person earns a few tens of thousands per year.

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But this does not accurately reflect what we mean when we're trying to discuss the "average" income. This is why the average income is almost always expressed by a different sort of average.

What are the three averages?

The three averages are:

• The "mean" is the "average" you're used to, where you add up all the numbers and then divide by the number of numbers.
• The "median" is the "middle" value in the list of numbers. To find the median, your numbers have to be listed in numerical order from smallest to largest, so you may have to rewrite your list before you can find the median.
• The "mode" is the value that occurs most often. If no number in the list is repeated, then there is no mode for the list.

The "range" of a list a numbers is just the difference between the largest and smallest values. It expresses "spread", being how far the values are distributed (or how concentrated they are).

• Find the mean, median, mode, and range for the following list of values:

13, 18, 13, 14, 13, 16, 14, 21, 13

The mean is the usual average, so I'll add and then divide:

(13 + 18 + 13 + 14 + 13 + 16 + 14 + 21 + 13) ÷ 9 = 15

Note that the mean, in this case, isn't a value from the original list. This is a common result. You should not assume that your mean will be one of your original numbers; you should not be surprised when it isn't.

The median is the middle value, so first I'll have to rewrite the list in numerical order:

13, 13, 13, 13, 14, 14, 16, 18, 21

There are nine numbers in the list, so the middle one will be the (9 + 1) ÷ 2 = 10 ÷ 2 = 5 th number:

So the median is 14 .

The mode is the number that is repeated more often than any other, so 13 , I see from my listing above, is the mode.

The largest value in the list is 21 , and the smallest is 13 , so the range is 21 − 13 = 8 .

mean: 15 median: 14 mode: 13 range: 8

Note: The formula for the place to find the median is " ( [the number of data points] + 1) ÷ 2 ", but you don't have to use this formula. You can just count in from both ends of the list until you meet in the middle, if you prefer, especially if your list is short. Either way will work.

The mean is the usual average:

(1 + 2 + 4 + 7) ÷ 4 = 14 ÷ 4 = 3.5

The median is the middle number. In this example, the numbers are already listed in numerical order, so I don't have to rewrite the list. But there is no "middle" number, because there are an even number of numbers.

Because of this, the median of the list will be the mean (that is, the usual average) of the middle two values within the list. The middle two numbers are 2 and 4 , so:

(2 + 4) ÷ 2 = 6 ÷ 2 = 3

So the median of this list is 3 , a value that isn't in the list at all.

The mode is the number that is repeated most often, but all the numbers in this list appear only once, so there is no mode.

The largest value in the list is 7 , the smallest is 1 , and their difference is 6 , so the range is 6 .

mean: 3.5 median: 3 mode: none range: 6

The values in the list above were all whole numbers, but the mean of the list was a decimal value. Getting a decimal value for the mean (or for the median, if you have an even number of data points) is perfectly okay; don't round your answers to try to match the format of the other numbers.

8, 9, 10, 10, 10, 11, 11, 11, 12, 13

The mean is the usual average, so I'll add up and then divide:

(8 + 9 + 10 + 10 + 10 + 11 + 11 + 11 + 12 + 13) ÷ 10 = 105 ÷ 10 = 10.5

The median is the middle value. In a list of ten values, that will be the (10 + 1) ÷ 2 = 5.5 -th value; the formula is reminding me, with that "point-five", that I'll need to average the fifth and sixth numbers to find the median. The fifth and sixth numbers are the last 10 and the first 11 , so:

(10 + 11) ÷ 2 = 21 ÷ 2 = 10.5

The mode is the number repeated most often. This list has two values that are repeated three times; namely, 10 and 11 , each repeated three times.

The largest value is 13 and the smallest is 8 , so the range is 13 − 8 = 5 .

mean: 10.5 median: 10.5 modes: 10 and 11 range: 5

As you can see, it is possible for two of the averages (the mean and the median, in this case) to have the same value. But this is not usual, and you should not expect it.

Note: Depending on your text or your instructor, the above data set may be viewed as having no mode rather than having two modes, because no single solitary number was repeated more often than any other. I've seen books that go either way on this; there doesn't seem to be a consensus on the "right" definition of "mode" in the above case. So if you're not certain how you should answer the "mode" part of the above example, ask your instructor before the next test.

How can I keep straight which average is which?

About the only hard part of finding the mean, median, and mode is keeping straight which "average" is which. Use this list:

• mean: regular meaning of "average"
• median: middle value
• mode: most often

(In the above, I've used the term "average" rather casually. The technical definition of what we commonly refer to as the "average" is technically called "the arithmetic mean": adding up the values and then dividing by the number of values. Since you're probably more familiar with the concept of "average" than with "measure of central tendency", I used the more comfortable term.)

• A student has gotten the following grades on his tests: 87, 95, 76, and 88 . He wants an 85 or better overall for the course. Assuming all tests are evenly weighted, what is the minimum grade he must get on the last test in order to achieve that overall average?

The minimum grade for the last test is what I need to find. To find the average of all his grades (the known ones, plus the unknown one), I have to add up all the grades, and then divide by the number of grades. Since I don't have a score for the last test yet, I'll use a variable to stand for this unknown value: " x ". Then, setting the expression for the average equal to the desired average, the computation is:

(87 + 95 + 76 + 88 + x ) ÷ 5 = 85

Multiplying through by 5 and simplifying, I get:

87 + 95 + 76 + 88 + x = 425

346 + x = 425

This is the score that he needs on the last test in order to get the overall grade that he is wanting. (If I doubt myself, I can always plug this value into the formula for the average, and confirm that I get 85 as the result.)

He needs to get at least a 79 on the last test.

You can use the Mathway widget below to practice finding the median. Try the entered exercise, or type in your own exercise. Or try entering any list of numbers, and then selecting the option — mean, median, mode, etc — from what the widget offers you. Then click the button to compare your answer to Mathway's.

Please accept "preferences" cookies in order to enable this widget.

(Click here to be taken directly to the Mathway site, if you'd like to check out their software or get further info.)

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Mean, Median, Mode, and Range Worksheets

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The word mean, which is a homonym for multiple other words in the English language, is similarly ambiguous even in the area of mathematics. Depending on the context, whether mathematical or statistical, what is meant by the "mean" changes. In its simplest mathematical definition regarding data sets, the mean used is the arithmetic mean, also referred to as mathematical expectation, or average. In this form, the mean refers to an intermediate value between a discrete set of numbers, namely, the sum of all values in the data set, divided by the total number of values. The equation for calculating the arithmetic mean is virtually identical to that for calculating the statistical concepts of population and sample mean, with slight variations in the variables used:

The mean is often denoted as x̄ , pronounced "x bar," and even in other uses when the variable is not x , the bar notation is a common indicator of some form of the mean. In the specific case of the population mean, rather than using the variable x̄ , the Greek symbol mu, or μ , is used. Similarly, or rather confusingly, the sample mean in statistics is often indicated with a capital X̄ . Given the data set 10, 2, 38, 23, 38, 23, 21, applying the summation above yields:

As previously mentioned, this is one of the simplest definitions of the mean, and some others include the weighted arithmetic mean (which only differs in that certain values in the data set contribute more value than others), and geometric mean . Proper understanding of given situations and contexts can often provide a person with the tools necessary to determine what statistically relevant method to use. In general, mean, median, mode and range should ideally all be computed and analyzed for a given sample or data set since they elucidate different aspects of the given data, and if considered alone, can lead to misrepresentations of the data, as will be demonstrated in the following sections.

The statistical concept of the median is a value that divides a data sample, population, or probability distribution into two halves. Finding the median essentially involves finding the value in a data sample that has a physical location between the rest of the numbers. Note that when calculating the median of a finite list of numbers, the order of the data samples is important. Conventionally, the values are listed in ascending order, but there is no real reason that listing the values in descending order would provide different results. In the case where the total number of values in a data sample is odd, the median is simply the number in the middle of the list of all values. When the data sample contains an even number of values, the median is the mean of the two middle values. While this can be confusing, simply remember that even though the median sometimes involves the computation of a mean, when this case arises, it will involve only the two middle values, while a mean involves all the values in the data sample. In the odd cases where there are only two data samples or there is an even number of samples where all the values are the same, the mean and median will be the same. Given the same data set as before, the median would be acquired in the following manner:

2,10,21, 23 ,23,38,38

After listing the data in ascending order, and determining that there are an odd number of values, it is clear that 23 is the median given this case. If there were another value added to the data set:

2,10,21, 23 , 23 ,38,38,1027892

Since there are an even number of values, the median will be the average of the two middle numbers, in this case, 23 and 23, the mean of which is 23. Note that in this particular data set, the addition of an outlier (a value well outside the expected range of values), the value 1,027,892, has no real effect on the data set. If, however, the mean is computed for this data set, the result is 128,505.875. This value is clearly not a good representation of the seven other values in the data set that are far smaller and closer in value than the average and the outlier. This is the main advantage of using the median in describing statistical data when compared to the mean. While both, as well as other statistical values, should be calculated when describing data, if only one can be used, the median can provide a better estimate of a typical value in a given data set when there are extremely large variations between values.

In statistics, the mode is the value in a data set that has the highest number of recurrences. It is possible for a data set to be multimodal, meaning that it has more than one mode. For example:

2,10,21,23,23,38,38

Both 23 and 38 appear twice each, making them both a mode for the data set above.

Similar to mean and median, the mode is used as a way to express information about random variables and populations. Unlike mean and median, however, the mode is a concept that can be applied to non-numerical values such as the brand of tortilla chips most commonly purchased from a grocery store. For example, when comparing the brands Tostitos, Mission, and XOCHiTL, if it is found that in the sale of tortilla chips, XOCHiTL is the mode and sells in a 3:2:1 ratio compared to Tostitos and Mission brand tortilla chips respectively, the ratio could be used to determine how many bags of each brand to stock. In the case where 24 bags of tortilla chips sell during a given period, the store would stock 12 bags of XOCHiTL chips, 8 of Tostitos, and 4 of Mission if using the mode. If, however, the store simply used an average and sold 8 bags of each, it could potentially lose 4 sales if a customer desired only XOCHiTL chips and not any other brand. As is evident from this example, it is important to take all manners of statistical values into account when attempting to draw conclusions about any data sample.

The range of a data set in statistics is the difference between the largest and the smallest values. While range does have different meanings within different areas of statistics and mathematics, this is its most basic definition, and is what is used by the provided calculator. Using the same example:

2,10,21,23,23,38,38 38 - 2 = 36

The range in this example is 36. Similar to the mean, range can be significantly affected by extremely large or small values. Using the same example as previously:

The range, in this case, would be 1,027,890 compared to 36 in the previous case. As such, it is important to extensively analyze data sets to ensure that outliers are accounted for.

PRACTICE PROBLEMS ON MEAN MEDIAN AND MODE

Problem 1 :

Find the (i) mean  (ii) median  (iii) mode for each of the following data sets :

a)  12, 17, 20, 24, 25, 30, 40

b)  8, 8, 8, 10, 11, 11, 12, 12, 16, 20, 20, 24

c)  7.9, 8.5, 9.1, 9.2, 9.9, 10.0, 11.1, 11.2, 11.2, 12.6, 12.9

d)  427, 423, 415, 405, 445, 433, 442, 415, 435, 448, 429, 427, 403, 430, 446, 440, 425, 424, 419, 428, 441

Problem 2 :

Consider the following two data sets :

Data set A : 5, 6, 6, 7, 7, 7, 8, 8, 9, 10, 12

Data set B : 5, 6, 6, 7, 7, 7, 8, 8, 9, 10, 20

a)  Find the mean for both Data set A and Data set B.

b)  Find the median of both Data set A and Data set B.

c)  Explain why the mean of Data set A is less than the mean of Data set B.

d)  Explain why the median of Data set A is the same as the median of Data set B

Problem 3 :

The table given shows the result when 3 coins were tossed simultaneously 40 times. The number of heads appearing was recorded.

Calculate the :   a)  mean     b)  median     c)  mode

Problem 4 :

The following frequency table records the number of text messages sent in a day by 50 fifteen-years-olds

a)  For this data, find the : (i) mean   (ii)  median   (iii)  mode

b)  construct a column graph for the data and show the position of the measures of centre (mean, median and mode) on the horizontal axis.

c)  Describe the distribution of the data.

d)  why is the mean smaller than the median for this data ?

e)  which measure of centre would be the most suitable for this data set ?

Problem 5 :

The frequency column graph alongside gives the value of donations for an overseas aid organisation, collected in a particular street.

a)  construct the frequency table from the graph.

b)  Determine the total number of donations.

c)  For the donations find the :  (i)  mean   (ii)  median   (iii)  mode

d) which of the measures of central tendency can be found easily from the graph only ?

Problem 6 :

Hui breeds ducks. The number of ducklings surviving for each pair after one month is recorded in the table.

a)  Calculate the : (i)  mean   (ii)  median   (iii) mode

b)  Is the data skewed ?

c)  How does the skewness of the data affect the measures of the middle of the distribution ?

Answers 

(c)  the mean of A is less than the mean of B.

(d)   median is the same.

(3)  (a)   Mean  =  1.4     (b)   median  =  1  (c)     mode  =  1

(4)  

(a)   (i)   Mean  =  5.74  (ii)     median  =  7  (iii)   mode  =  8

(c)     bimodal data.

The mean takes into account the full range of numbers of text messages and is affected by extreme values. Also, the value which is lower than the median is well below it.

(e)   The median

(5)  

(b)   ∑f  =  30

(c)  (i)   Mean  =  $2.9  (ii)   median  =  $2  (iii)   mode  =  $2

(6)  

(a)  (i)  Mean  =  4.25    (ii)   median  =  5   (iii)   mode  =  5

c)   By observing the graph, the mean is less than the median and mode.

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Mean, Median, Mode and Range Worksheets Math Problems

Subject: Mathematics

Age range: 7-11

Resource type: Worksheet/Activity

Last updated

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Mean, Median, Mode and Range Worksheets Math Problems “Mean, Median & Mode Worksheets Math Problems” offers a comprehensive resource for students to master these fundamental statistical concepts. This product includes a variety of engaging worksheets designed to reinforce understanding and application of mean, median, and mode in real-world scenarios. Diverse Problem Sets: Each worksheet contains a range of problems, from basic to advanced, ensuring students can progressively build their skills. Real-Life Context: Problems are contextualized within everyday situations, helping students grasp the practical significance of mean, median, and mode. Answer Keys: Detailed answer keys are provided for easy assessment and self-correction, promoting independent learning. Extension Activities: Extension exercises challenge students to apply their knowledge in more complex scenarios, fostering critical thinking and problem-solving skills. Whether used in the classroom or for independent study, “Mean, Median & Mode Worksheets Math Problems” equips students with the tools they need to confidently navigate statistical analysis and interpretation. Worksheets are made in 8.5” x 11” Standard Letter Size. This resource is helpful in students’ assessment, Independent Studies, group activities, practice and homework. This product is available in PDF format and ready to print as well.

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Teachers are Terrific

Ways to Combine Math, STEM, & Fun!

May 5, 2024 by Carol Davis

Let’s combine an exciting STEM Challenge and collecting data. Students will use data to calculate the mean, median, mode, and range after completing each task!

This is all about cup stacking!

Now, you know this is true >>> If you give a group of students a stack of cups, they will immediately take them apart and start building pyramids. #right

So, why not add some math to the task and practice solving problems, too!

“ In this post, for your convenience, you may find Amazon Affiliate links to resources. This means that Amazon will pass on small percentages to me with your purchase of items. This will not create extra costs for you at all! It will help me keep this blog running! “

Cups and Math, Really?

I know you are wondering how on earth putting some cups out is going to end up with math activities, just take a look at all we can do!

• It’s fun, first of all. Since it appears to be a game and a competition, it is very engaging.
• The math includes finding the mean, median, range, and mode of the data collected.
• It includes class data charts that result in math problems.
• Did I mention that it is fun?

Cups and Math Exploration

We always begin with just a free-stacking time. Students can build any shape and height until they run out of cups. I give them about 5 minutes. Then we get busy.

TIP : Use plastic or paper cups. Foam cups can have static and the cups will move and crash when that static effect happens.

TIP : Set up some rules- My biggest rule is that when I hit the light switch student must stop building!

STEM and Math Task 1

The first assignment is to build the tallest tower possible using as many cards as possible in a certain amount of time.

When the timer dings students count their cups in the tower and report it to the class data keeper.

Every team then completes the lab sheet by calculating the mean, median, mode, and range of the class data.

TIP : Make sure students know how to perform these functions before beginning. I review mean (averaging) and show students how to calculate the others. I have an anchor chart that reminds them what to do for each calculation.

Different Shapes

For our beginning task, almost all groups will make a traditional pyramid with a long straight line of cups.

However, one of the later tasks asks students to make the bottom row into a different shape.

Notice the circular shape of the one in the photo!

More Cups and Math

A couple of the tasks have students counting the cups for their data tables.

But, two of the tasks ask them to build a tower and measure its height.

We calculate the same mean, median, range, and mode with those measurements.

I told you this was all about math skills!

Data Tables for STEM and Math Tasks

This resource has the student data tables already made for them.

For our class data table, I just project one of these pages onto our whiteboard and students fill in their info with a dry-erase marker.

It also works to have a recorder chosen to write numbers on the chart while you are measuring the towers.

FINAL TIP : We use calculators for this activity. That is optional for your students, of course! I do it because our class time is limited and it just takes longer for students to add and divide.

So, I know you are wondering how this is a design project! Do you remember those towers I mentioned that students build using different shapes? Those shapes are a lot harder than you would think. The base is the easiest part but the next layers are very tricky. The base must be built well in order to support more rows. Also, students are always competing in this challenge, and building fancy, wonky shapes inevitably ends in a tremendous crash.

Try this challenge if your kids love competing and you love adding some math to your cup stacking!

STEM and Math fit together perfectly. This is a fun challenge that will produce interesting results and lots of learning! (Not to mention the practice of finding those results.)

More math-related projects can be found in these blog posts:

• The Bottle Flip Challenge
• Barbie Bungee Jump

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