Grade 7 Math Practice Test: Comparing Two Data Sets (Mean, Median and MAD)
- Comparing Data Sets
- 10 questions
- 15 minutes
This test covers measures of center and variability and how to use them to compare two groups. Tip: to judge how far apart two groups are, compare the difference of their means with their mean absolute deviation (MAD).
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Question 1
What is the mean of 12, 15, 9, 14 and 10?
Correct answer: D
The sum is 60 and there are 5 values, so the mean is 60 ÷ 5 = 12.
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Question 2
What is the mean absolute deviation (MAD) of 4, 6, 8, 10 and 12?
Correct answer: C
The mean is 8. The distances from 8 are 4, 2, 0, 2 and 4, which add to 12, and 12 ÷ 5 = 2.4. 0 comes from adding signed differences, which always cancel out.
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Question 3
Class A has a mean quiz score of 82 with a MAD of 4. Class B has a mean of 74 with a MAD of 4. The difference of the means is how many times the MAD?
Correct answer: D
The means differ by 82 − 74 = 8, and 8 ÷ 4 = 2. 8 is the difference itself, not a multiple of the MAD.
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Question 4
Two classes have the same mean test score. Class A has a MAD of 3 points and Class B has a MAD of 9 points. Which statement is true?
Correct answer: B
A larger MAD means the scores are farther from the mean on average, so Class B's scores vary more. The MAD says nothing about which class scored higher or about class size.
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Question 5
What is the median of 8, 3, 10, 5, 12, 6?
Correct answer: A
In order: 3, 5, 6, 8, 10, 12. The two middle values are 6 and 8, so the median is 7. 7.5 averages the middle values of the unsorted list.
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Question 6
The ages of five people at a party are 20, 22, 23, 25 and 90. Which measure best describes a typical age, and why?
Correct answer: C
The mean is 36, older than four of the five people, because the outlier 90 pulls it up. The median 23 is not affected by the outlier. The range measures spread, not a typical value.
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Question 7
What is the interquartile range (IQR) of 2, 4, 5, 7, 8, 10, 12, 15?
Correct answer: B
The lower half 2, 4, 5, 7 has median 4.5, and the upper half 8, 10, 12, 15 has median 11. IQR = 11 − 4.5 = 6.5. 13 is the range.
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Question 8
A school surveys a random sample of 20 seventh graders and 20 eighth graders about hours of sleep. The median is 8.5 hours for the seventh graders and 7.5 hours for the eighth graders, and the spreads are similar. Which inference is reasonable?
Correct answer: A
Random samples can support a general comparison, and the seventh graders’ median is higher. They cannot show that every single seventh grader sleeps more.
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Question 9
Group A has 10 students with a mean of 6 books read. Group B has 15 students with a mean of 8 books read. What is the mean for all 25 students?
Correct answer: C
Total books: 10 × 6 + 15 × 8 = 60 + 120 = 180, and 180 ÷ 25 = 7.2. 7 is the average of 6 and 8, which ignores that Group B is larger.
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Question 10
The mean of five test scores is 80. Four of the scores are 72, 85, 90 and 78. What is the fifth score?
Correct answer: A
The five scores must add to 5 × 80 = 400. The four known scores add to 325, so the fifth is 75. 81.25 is the mean of the four known scores.
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