Question

using box plots to compare data distributions
the box plots show the distributions of daily
temperatures, in °f, for the month of january for two
cities.
which statements are true about the distributions?
check all that apply.
cedar rapids
longview
both distributions are symmetric.
both distributions are skewed right.
both distributions are skewed left.
the mean and standard deviation would be the
best measures to compare the data.
the median and iqr would be the best measures
to compare the data.

Explanation:

Step1: Analyze the box - plots for skewness

Box - plots show the distribution's shape. If the median is not in the center of the box and the whiskers are of unequal length, the distribution is skewed. For Cedar Rapids, the lower whisker is longer (data is more spread out on the lower end), so it is skewed left. For Longview, the upper whisker is longer (data is more spread out on the upper end), so it is skewed right. So the statement “Both distributions are skewed” is incorrect.

Step2: Determine the appropriate measures of central tendency and spread

When distributions are skewed (as these box - plots suggest), the median (a measure of central tendency) and the inter - quartile range (IQR, a measure of spread) are more robust measures. The mean and standard deviation are sensitive to extreme values (which are more of a concern in skewed distributions).

Answer:

The median and IQR would be the best measures to compare the data.