Comparing two populations worksheet

Grade 7 math, Common Core 7.SP.B.3. 8 problems with an answer key and worked steps. Free to print, and you can make new problems any time.

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Comparing two populations

Grade 7 math, Common Core 7.SP.B.3

Compare the two groups. MAD stands for mean absolute deviation.

1.
Minutes of reading. Group A: 10, 24, 26, 11, 17. Group B: 14, 26, 31, 12, 18. Which group read more, on average, and by how much?
2.
The first garden bed has a mean plant height in cm of 63, and the second bed has a mean of 75. Both have a MAD of 6. How many MADs apart are the means?
3.
Minutes of reading. Group A: 29, 14, 28, 16, 30. Group B: 37, 22, 33, 21, 34. Which group read more, on average, and by how much?
4.
Class A has a mean test score of 65, and Class B has a mean of 70. Both have a MAD of 2. How many MADs apart are the means?
5.
Class A has a mean test score of 72, and Class B has a mean of 77. Both have a MAD of 5. How many MADs apart are the means?
6.
Team Red has a mean points per game of 59, and Team Blue has a mean of 61. Both have a MAD of 2. How many MADs apart are the means?
7.
The first garden bed has a mean plant height in cm of 54, and the second bed has a mean of 61.5. Both have a MAD of 5. How many MADs apart are the means?
8.
Minutes of reading. Group A: 28, 18, 24, 19, 24. Group B: 32, 24, 30, 26, 28. Which group read more, on average, and by how much?

Answer key: Comparing two populations

Grade 7 math. Each answer has a few worked steps, to help check the method as well as the answer.

1. Group B, by 2.6 minutes (means 17.6 and 20.2)
Mean A: 88 ÷ 5 = 17.6Mean B: 101 ÷ 5 = 20.2
2. 2 MADs
Difference: 75 − 63 = 1212 ÷ 6 = 2
3. Group B, by 6 minutes (means 23.4 and 29.4)
Mean A: 117 ÷ 5 = 23.4Mean B: 147 ÷ 5 = 29.4
4. 2.5 MADs
Difference: 70 − 65 = 55 ÷ 2 = 2.5
5. 1 MADs
Difference: 77 − 72 = 55 ÷ 5 = 1
6. 1 MADs
Difference: 61 − 59 = 22 ÷ 2 = 1
7. 1.5 MADs
Difference: 61.5 − 54 = 7.57.5 ÷ 5 = 1.5
8. Group B, by 5.4 minutes (means 22.6 and 28)
Mean A: 113 ÷ 5 = 22.6Mean B: 140 ÷ 5 = 28

The answer key prints on its own page. You’re welcome to print and copy these worksheets for your own kids or class.

About comparing two populations

To compare two groups, look at a measure of center (mean or median) and a measure of spread (MAD or interquartile range). When the spreads are similar, you can describe the gap between the centers as a multiple of the spread: a difference of 2 MADs is a big, meaningful gap.

Worked example 1

Minutes of reading. Group A: 26, 22, 13, 22, 18. Group B: 34, 32, 22, 29, 28. Which group read more, on average, and by how much?

Step 1.Mean A: 101 ÷ 5 = 20.2
Step 2.Mean B: 145 ÷ 5 = 29

Answer: Group B, by 8.8 minutes (means 20.2 and 29)

Worked example 2

The morning class has a mean quiz score of 78, and the afternoon class has a mean of 96. Both have a MAD of 6. How many MADs apart are the means?

Step 1.Difference: 96 − 78 = 18
Step 2.18 ÷ 6 = 3

Answer: 3 MADs

Worked example 3

Class A has a mean test score of 73, and Class B has a mean of 79. Both have a MAD of 6. How many MADs apart are the means?

Step 1.Difference: 79 − 73 = 6
Step 2.6 ÷ 6 = 1

Answer: 1 MADs

Watch out for

Compare like with like: mean with mean, median with median.
Divide the difference in means by the MAD to see how many MADs apart they are.
A big overlap means the groups are not very different.

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