Question

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. 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 shape of box - plots

A symmetric box - plot has the median in the middle of the box and the whiskers of approximately equal length. A skewed - right box - plot has a longer right whisker and the median closer to the left side of the box. A skewed - left box - plot has a longer left whisker and the median closer to the right side of the box.
Looking at the box - plots of Longview and Cedar Rapids, we can see that both have longer left whiskers. So, both distributions are skewed left.

Step2: Determine the best measures of central tendency and spread

When the data is skewed, the median (a measure of central tendency) and the inter - quartile range (IQR, a measure of spread) are more appropriate. The mean is sensitive to extreme values (in the skewed tail) and the standard deviation is also affected by skewness.

Answer:

• Both distributions are skewed left.
• The median and IQR would be the best measures to compare the data.