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

Explanation:

Step1: Recall box - and - whisker plot properties

In a box - and - whisker plot, the first quartile ($Q_1$) is at the left - hand edge of the box, the median ($Q_2$) is the line inside the box, and the third quartile ($Q_3$) is at the right - hand edge of the box. The minimum value is at the left - hand end of the whisker, and the maximum value is at the right - hand end of the whisker. Here, $Q_1 = 6$ and $Q_3=15$. The inter - quartile range (IQR) contains 50% of the data values. The value 13 is between $Q_1$ and $Q_3$.

Step2: Determine the percentage of data

Since the inter - quartile range (the range from $Q_1$ to $Q_3$) contains 50% of the data values, and 6 is $Q_1$ and 13 is between $Q_1$ and $Q_3$, and 13 is closer to $Q_3$ than to $Q_1$. We know that the data between $Q_1$ and $Q_3$ is 50% of the data set. Since 13 is closer to $Q_3$ (15), we can estimate that the percentage of data between 6 and 13 is approximately 37.5%. We assume a relatively even distribution within the IQR. The distance from 6 to 15 is 9 units, and the distance from 6 to 13 is 7 units. $\frac{7}{9}\times50%\approx37.5%$.

Answer:

37.5%