Question

what can you tell about the means for these two months? (2 points)
a the august high is above the july median. this makes it hard to know about the means.
b both months have the same low temperature. this makes it hard to know about the means.
c it is unlikely, but possible that the july mean could be higher.
d there is no way to tell what the means are.

Explanation:

Step1: Analyze the box - and - whisker plots

A box - and - whisker plot shows the minimum, first quartile, median, third quartile, and maximum of a data set. The mean is calculated by summing all data points and dividing by the number of data points. The box - and - whisker plot does not provide information about the individual data points (except for the five - number summary).

Step2: Consider the relationship between median and mean

The median is the middle value when the data is ordered. The mean is affected by all data values. Just knowing the median (from the box - and - whisker plot) is not sufficient to calculate the mean. For example, if we have two data sets with the same median:
Set 1: \(1, 2, 3\) (median \(= 2\), mean \(=\frac{1 + 2+3}{3}=2\))
Set 2: \(1, 2, 10\) (median \(= 2\), mean \(=\frac{1 + 2 + 10}{3}=\frac{13}{3}\approx4.33\))

Answer:

d. There is no way to tell what the means are.