Box Plot X has a taller box than Box Plot Y. What does this indicate about the data in Box Plot X compared to Box Plot Y?

Greater variability in the middle 50% of the data.

Less variability in the middle 50% of the data.

Greater variability in the extreme values of the data.

Less variability in the extreme values of the data.

Data Set P has whiskers from 10 to 20 and 50 to 60. Data Set Q has whiskers from 30 to 32 and 38 to 40. Which statement correctly compares their variability?

Set P shows greater variability in its extreme values.

Set Q shows greater variability in its extreme values.

Both sets show equal variability in their extreme values.

The variability cannot be compared without the medians.

Make Comparative Inferences About Populations Practice — Grade 7 math

Lesson 3: Make Comparative Inferences About Populations — Practice Questions

1. Box Plot X has a taller box than Box Plot Y. What does this indicate about the data in Box Plot X compared to Box Plot Y?
- A. Greater variability in the middle 50% of the data.
- B. Less variability in the middle 50% of the data.
- C. Greater variability in the extreme values of the data.
- D. Less variability in the extreme values of the data.
2. A box plot shows a first quartile ($Q_1$) of 15 and a third quartile ($Q_3$) of 35. The interquartile range, which determines the height of the box, is ___.
3. A data set's box plot shows an interquartile range of 25. If the first quartile ($Q_1$) is 40, what is the value of the third quartile ($Q_3$)? The value is ___.
4. Data Set P has whiskers from 10 to 20 and 50 to 60. Data Set Q has whiskers from 30 to 32 and 38 to 40. Which statement correctly compares their variability?
- A. Set P shows greater variability in its extreme values.
- B. Set Q shows greater variability in its extreme values.
- C. Both sets show equal variability in their extreme values.
- D. The variability cannot be compared without the medians.
5. Box Plot A has quartiles $Q_1 = 30$ and $Q_3 = 50$. Box Plot B has quartiles $Q_1 = 35$ and $Q_3 = 45$. Which plot shows greater variability in the middle 50% of its data?
- A. Box Plot A
- B. Box Plot B
- C. They have equal variability
- D. Cannot be determined
6. Team A has a median score of 72 and an IQR of 20. Team B has a median of 65 and an IQR of 5. Which conclusion is best supported by this data?
- A. Team A scores higher on average and is more consistent.
- B. Team A scores higher on average, but Team B is more consistent.
- C. Team B scores higher on average and is more consistent.
- D. Both teams perform equally because their spreads overlap.
7. Runner X has a median finish time of 48 seconds and a Standard Deviation of 3 seconds. Runner Y has a median of 52 seconds and a Standard Deviation of 1 second. The runner with more **consistent** performance is Runner ___.
8. Store A and Store B both have a median daily revenue of 3,000 dollars. Store A has a Range of 4,000 dollars and Store B has a Range of 800 dollars. What is the most valid conclusion?
- A. Store A is more reliable because its revenue is higher on peak days.
- B. Store B is more predictable because it has a smaller range.
- C. Both stores perform identically since their medians are equal.
- D. Store A is more consistent because its range includes more values.
9. Which statement about comparing two data sets is statistically incomplete?
- A. "Group A has a higher median (90 vs 82) and a larger IQR (18 vs 7)."
- B. "Group B is more consistent with a lower Standard Deviation (4 vs 11)."
- C. "Group A performed better because its median is higher."
- D. "Group B has a lower median but is more reliable due to its smaller IQR."
10. Student 1 scores 60 and 90 on two tests. Student 2 scores 74 and 76. Both students have the same mean of 75. The student with more **variable** performance is Student ___.