the following data are the ages (in years) of 17 statistics teachers in a school district. 53, 52, 53, 47…

Explanation:

Step1: Arrange data in ascending order

27, 28, 31, 35, 36, 37, 38, 47, 47, 51, 51, 52, 53, 53, 58, 59, 60

Step2: Find the minimum value

The minimum value is 27.

Step3: Find the first - quartile ($Q_1$)

Since $n = 17$, the position of $Q_1$ is $\frac{n + 1}{4}=\frac{17+1}{4}=4.5$. So $Q_1=\frac{35 + 36}{2}=35.5$.

Step4: Find the median ($Q_2$)

The position of the median is $\frac{n + 1}{2}=\frac{17+1}{2}=9$. So the median $Q_2 = 47$.

Step5: Find the third - quartile ($Q_3$)

The position of $Q_3$ is $\frac{3(n + 1)}{4}=\frac{3\times(17 + 1)}{4}=13.5$. So $Q_3=\frac{53+53}{2}=53$.

Step6: Find the maximum value

The maximum value is 60.

Answer:

To construct the box - and - whisker plot:

• The left - most point (the end of the left whisker) is at 27.
• The left side of the box is at $Q_1 = 35.5$.
• The line inside the box is at the median $Q_2=47$.
• The right side of the box is at $Q_3 = 53$.
• The right - most point (the end of the right whisker) is at 60.