Question

the following data are the ages (in years) of 19 economics teachers in a school district. 39, 57, 48, 47, 49, 24, 36, 54, 34, 30, 33, 35, 31, 38, 43, 23, 38, 32, 60 send data to calculator send data to excel using the tool provided, construct a box - and - whisker plot (sometimes called a boxplot) for the data.

Explanation:

Step1: Sort the data

23, 24, 30, 31, 32, 33, 34, 35, 36, 38, 38, 39, 43, 47, 48, 49, 54, 57, 60

Step2: Find the minimum value

The minimum value is 23.

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

There are $n = 19$ data points. The position of $Q_1$ is $\frac{n + 1}{4}=\frac{19+1}{4}=5$. So $Q_1$ is the 5th - ordered value, which is 32.

Step4: Find the median ($Q_2$)

The position of the median is $\frac{n + 1}{2}=\frac{19+1}{2}=10$. So the median $Q_2$ is 38.

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

The position of $Q_3$ is $\frac{3(n + 1)}{4}=\frac{3\times(19 + 1)}{4}=15$. So $Q_3$ is 48.

Step6: Find the maximum value

The maximum value is 60.

Step7: Construct the box - and - whisker plot

Draw a number line that includes the range from 23 to 60. Draw a box from $Q_1 = 32$ to $Q_3=48$, draw a vertical line inside the box at the median $Q_2 = 38$. Draw whiskers from the box to the minimum value 23 and the maximum value 60.

Answer:

The box - and - whisker plot is constructed with minimum = 23, $Q_1=32$, median = 38, $Q_3 = 48$, maximum = 60.