Question

the data distributions below show the running times of a group of runners before and after training for a marathon.
before training after training
which statement correctly explains the summary statistics that should be used to compare the running times?
a. the distributions are normal, so the mean and standard - deviation should be used to compare the running times.
b. the distributions are skewed, so the mean and standard deviation should be used to compare the running times.
c. the distributions are normal, so the median and interquartile range should be used to compare the running times.
d. the distributions are skewed, so the median and interquartile range should be used to compare the running times.

Explanation:

Step1: Identify distribution shape

The histograms of running - times before and after training are bell - shaped, which indicates normal distributions.

Step2: Recall summary statistics for normal distributions

For normal distributions, the mean and standard deviation are the appropriate summary statistics to use for comparison as they capture the center and spread of the data well.

Answer:

A. The distributions are normal, so the mean and standard deviation should be used to compare the running times.