Question

Students in a fitness class each completed a one-mile walk or run. The list shows the time it took each person to complete the mile. Each time is rounded to the nearest half-minute.

5.5, 6, 7, 10, 7.5, 8, 9.5, 9, 8.5, 8, 7, 7.5, 6, 6.5, 5.5

Which statements are true about a histogram with one-minute increments representing the data? Select three options.

A. A histogram will show that the mean time is approximately equal to the median
time of 7.5 minutes.
B. The histogram will have a shape that is left-skewed.
C. The histogram will show that the mean time is greater than the median time of 7.4
minutes.
D. The shape of the histogram can be approximated with a normal curve.
E. The histogram will show that most of the data is centered between 6 minutes and
9 minutes.

Answer 1

Explanation:

Option A, Option C, and Option E are possible statements that could be true about a histogram with one-minute increments representing the given data.

A. A histogram will show that the mean time is approximately equal to the median time of 7.5 minutes: This statement is possible as the data set appears to be roughly symmetric, with no apparent skewness. Therefore, the histogram is likely to have a roughly normal distribution, and the mean and median will be close to each other.

B. The histogram will have a shape that is left-skewed: This statement is unlikely to be true as the data set does not have any significant outliers on the left side to cause a strong skewness to the left.

C. The histogram will show that the mean time is greater than the median time of 7.4 minutes: This statement is possible as the data set contains a few relatively large values (e.g., 10) that could pull the mean to the right of the median.

D. The shape of the histogram can be approximated with a normal curve: This statement is unlikely to be true as the data set is relatively small, and the histogram with one-minute increments is likely to show some variability.

E. The histogram will show that most of the data is centered between 6 minutes and 9 minutes: This statement is possible as most of the values in the data set fall within this range, and there are no apparent outliers that would cause the center to shift significantly.