Question

which of the following statements about the box - and - whisker plot below is not true?
both 72 and 99 are values in the set of data.
the median of the data set shown is 81.
there are fewer data points in the lower two quartiles than in the upper two quartiles.
the midrange of the data set shown is 85.5.

Explanation:

Step1: Analyze the box - and - whisker plot

In a box - and - whisker plot, the whiskers represent the minimum and maximum values. Here, the minimum value is 72 and the maximum value is 99. So, both 72 and 99 are values in the data set.

Step2: Determine the median

The line inside the box represents the median. From the plot, the median is 81.

Step3: Check the number of data points in quartiles

In a box - and - whisker plot, each quartile contains 25% of the data. So, the lower two quartiles (first and second) contain 50% of the data and the upper two quartiles (third and fourth) also contain 50% of the data.

Step4: Calculate the midrange

The midrange is calculated as \(\frac{\text{Minimum}+\text{Maximum}}{2}\). Substituting the values (minimum = 72, maximum = 99), we get \(\frac{72 + 99}{2}=\frac{171}{2}=85.5\)

Answer:

The statement “There are fewer data points in the lower two quartiles than in the upper two quartiles” is not true.