Question

the box plots show the distributions of the numbers of words per line in an essay printed in two different fonts
number of words per line
font 1
font 2
0 2 4 6 8 10 12 14 16 18 20 22 24 26 28
which measure of center would be best to compare the data sets?
the median is the best measure because both distributions are left - skewed.
the mean is the best measure because both distributions are left - skewed.
the median is the best measure because both distributions are symmetric.
the mean is the best measure because both distributions are symmetric.

Explanation:

1. Recall the properties of mean and median: The mean is affected by skewness and outliers, while the median is a resistant measure (less affected by skewness/outliers).
2. Analyze the box - plots: The left - skewed (negatively skewed) distribution has a long tail on the left. For left - skewed distributions, the mean is pulled towards the tail (left side), so the median is a better measure of center as it represents the middle value more accurately.
3. Evaluate the options:

• Option 1: Says the median is best because both distributions are left - skewed. This matches the property that median is better for skewed data.
• Option 2: The mean is not best for left - skewed data as it is affected by the skewness, so this is wrong.
• Option 3: The distributions are left - skewed, not symmetric, so this is wrong.
• Option 4: The distributions are left - skewed, not symmetric, and mean is not best for skewed data, so this is wrong.

Answer:

A. The median is the best measure because both distributions are left - skewed.