Comparing Two Populations: Grade 7 Math Test – PDF Download

Question 1: Median and IQR (2 points)

The data show the number of cans collected by seven classes: 31, 27, 35, 40, 29, 38, and 33. Find the median and the interquartile range (IQR).

Question 2: Two practice groups (3 points)

The dot plots show free throws made out of 10 by players in two practice groups.

1. Find the mean of each group. (1 point)
2. Find the MAD of each group. (1 point)
3. Write the difference of the means as a multiple of the MAD. (1 point)

Question 3: Text messages (2 points)

Two random samples of students sent text messages in one day. The first sample has a mean of 48 messages and the second has a mean of 66 messages. Both samples have a MAD of 9 messages.

1. Write the difference of the means as a multiple of the MAD. (1 point)
2. Suppose both MADs were 6 messages instead. Write the new multiple. (1 point)

Question 4: Biking clubs (3 points)

The box plots show the miles biked in one week by random samples of members of two clubs.

1. Find the median of each club and the difference of the medians. (1 point)
2. Find the IQR of each club. (1 point)
3. Do the boxes overlap? Explain. (1 point)

Question 5: Typing speeds (3 points)

The dot plots show the words typed per minute by random samples from two classes. Both samples have a MAD of 2 words per minute.

1. Find the mean of each class. (1 point)
2. Write the difference of the means as a multiple of the MAD. (1 point)
3. Describe the overlap of the two distributions. (1 point)

Question 6: Pages read (3 points)

Mei asked a random sample of 8 sixth graders and a random sample of 8 seventh graders how many pages they read last week.

Sixth grade: 23, 24, 27, 30, 31, 34, 34, 37.

Seventh grade: 32, 33, 34, 37, 38, 42, 42, 46.

1. Find the mean and MAD of each sample. (2 points)
2. Write a sentence that compares the two grades, using the multiple of the MAD. (1 point)

Question 7: Find the error (2 points)

Group A has a mean of 70 and a MAD of 5. Group B has a mean of 80 and a MAD of 5. Jamal says, “Group B is 10 MADs higher than Group A.” Explain Jamal’s mistake and give the correct multiple.

Question 8: Working backward (2 points)

Two samples have means of 120 and 150 and the same MAD. The difference of the means is 2.5 times the MAD.

1. Find the MAD. (1 point)
2. A third sample has a mean that is 1.5 MADs above 150. Find its mean. (1 point)

⬇ Download the Grade 7 Comparing Two Populations test (PDF, 78 KB)

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