Question

what percentage of the data values falls between the values of 3 and 24 in the data set shown?

Explanation:

Step1: Recall the properties of a box - and - whisker plot

In a box - and - whisker plot, the left - most point is the minimum value, the right - most point is the maximum value. The box starts at the first quartile ($Q_1$) and ends at the third quartile ($Q_3$). The line inside the box is the median ($Q_2$).
The value 3 is the minimum value (left - most point) and 24 is the maximum value (right - most point) of the data set.

Step2: Use the percentage formula for data within the range of minimum and maximum

The formula for the percentage of data within the range of minimum ($x_{\text{min}}$) and maximum ($x_{\text{max}}$) is \(P=\frac{x_{\text{max}}-x_{\text{min}}}{x_{\text{max}}-x_{\text{min}}}\times100\%\)
Since \(x_{\text{min}} = 3\) and \(x_{\text{max}}=24\), and the range from \(x_{\text{min}}\) to \(x_{\text{max}}\) contains all the data points.

Answer:

100%