Question

the box - and - whisker plot below represents some data set. what percentage of the data values are between 8 and 18?

Explanation:

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

In a box - and - whisker plot, the left end of the box is the first quartile ($Q_1$), the right end of the box is the third quartile ($Q_3$), and the median is the line inside the box. The whiskers represent the minimum and maximum values. The inter - quartile range (IQR) is $Q_3 - Q_1$. The data between $Q_1$ and $Q_3$ represents 50% of the data. Also, the distance from the minimum to $Q_1$ and from $Q_3$ to the maximum each represent 25% of the data.

Here, 8 is the minimum value and 18 is $Q_1$ (the left - hand side of the box). The box (from $Q_1$ to $Q_3$) represents 50% of the data, and the part from the minimum to $Q_1$ represents 25% of the data.

Step2: Calculate the percentage

We want the percentage of data between 8 (minimum) and 18 ($Q_1$).
Since the part from the minimum to $Q_1$ in a box - and - whisker plot represents 25% of the data.

Answer:

25%