Question

the box plots show the distributions of the numbers of words per line in an essay printed in two different fonts. which measure of center would be best to compare the data sets?
o the median is the best measure because both distributions are left - skewed.
o the mean is the best measure because both distributions are left - skewed.
o the median is the best measure because both distributions are symmetric.
o the mean is the best measure because both distributions are symmetric.

Explanation:

Step1: Recall the properties of mean and median

The median is less affected by outliers and skewed data. The mean is affected by outliers.

Step2: Analyze the box - plots

Looking at the box - plots, we need to check the skewness. A symmetric distribution has the median and mean in a certain relationship. But if the distribution is skewed, the median is a better measure.

Step3: Check the skewness of the distributions

Since the problem is about comparing two data sets using a measure of center. If the distributions are symmetric, mean and median can be considered. But if we assume (from the general property of box - plots and measure of center selection) that when we want a robust measure (not affected by extreme values), median is better. And if the data is symmetric, both mean and median can represent the center. But in the absence of clear symmetry indication (and in the context of box - plots, median is a common measure for non - symmetric or when we want to avoid outlier influence).

Answer:

The median is the best measure because both distributions are symmetric.