Question

number of coupon users per hour
day 1
day 2
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
which measure of variability can be compared using the box plots?
standard deviation
mean
interquartile range
median

Explanation:

1. Recall what box - plots represent: A box - plot shows the minimum, first quartile ($Q_1$), median, third quartile ($Q_3$), and maximum of a data set.
2. Analyze each option:

• Standard deviation: Box - plots do not directly show information about standard deviation. Standard deviation is a measure of how far data points are from the mean, and box - plots are based on quartiles, not the mean - centered spread in the same way as standard deviation.
• Mean: The mean is not a measure of variability (it is a measure of central tendency), and box - plots are mainly used to show the spread (variability) and median (central tendency), not the mean.
• Interquartile range (IQR): The interquartile range is calculated as $IQR = Q_3 - Q_1$. In a box - plot, the length of the box represents the interquartile range (from $Q_1$ to $Q_3$). So we can compare the interquartile range of two data sets (like Day 1 and Day 2 here) using their box - plots by looking at the length of the boxes.
• Median: The median is a measure of central tendency, not variability. The line inside the box in a box - plot represents the median, but it does not measure variability.

Answer:

interquartile range