Chapter 12.4, Problem 25PPE

To determine

To find: The mean, median, and mode of a data set by looking at the box-and-whisker plot.

Explanation of Solution

Given information:

Need to explain if the mean, median, and mode of a data set can be derived by looking at the box-and-whisker plot.

Calculation:

Quartiles are the value which divided a data set into four equal parts. Median represents second quartile $\left(Q_2\right)$ and divided data set into two equal halves. First quartile $\left(Q_1\right)$ is the median of lower half of data and third quartile $\left(Q_3\right)$ is the median of upper half of data set.

Here third quartile is equal to the maximum value. Hence, it is not mandatory to have third quartile always less than maximum data value. It can be equal as well.

A box-and-whisker plot is shown below. The box portion of the plot represents interquartile range.

  

By looking at the box-and-whisker plot median can be found but mean and mode cannot be derived.