Question

the following are the ages of 18 history teachers in a school district. 28, 29, 31, 32, 34, 37, 38, 39, 39, 44, 44, 46, 50, 51, 53, 53, 54, 57. notice that the ages are ordered from least to greatest. make a box - and - whisker plot for the data.

Explanation:

Step1: Find the minimum value

The minimum value of the data - set is 28.

Step2: Find the first quartile ($Q_1$)

There are $n = 18$ data points. The position of $Q_1$ is $\frac{n + 1}{4}=\frac{18+1}{4}=4.75$. So, $Q_1$ is the value at the 4.75 - th position. Interpolating between the 4 - th and 5 - th ordered values: The 4 - th value is 32 and the 5 - th value is 34. $Q_1=32+(34 - 32)\times0.75=32 + 1.5=33.5$.

Step3: Find the median ($Q_2$)

The position of the median is $\frac{n+1}{2}=\frac{18 + 1}{2}=9.5$. Interpolating between the 9 - th and 10 - th ordered values: The 9 - th value is 39 and the 10 - th value is 44. $Q_2=39+(44 - 39)\times0.5=39 + 2.5=41.5$.

Step4: Find the third quartile ($Q_3$)

The position of $Q_3$ is $\frac{3(n + 1)}{4}=\frac{3\times(18+1)}{4}=14.25$. Interpolating between the 14 - th and 15 - th ordered values: The 14 - th value is 51 and the 15 - th value is 53. $Q_3=51+(53 - 51)\times0.25=51+0.5 = 51.5$.

Step5: Find the maximum value

The maximum value of the data - set is 57.

Step6: Plot the box - and - whisker plot

On the number line:

• Mark the minimum value (28) with a dot.
• Draw a box from $Q_1 = 33.5$ to $Q_3=51.5$.
• Draw a vertical line inside the box at the median $Q_2 = 41.5$.
• Draw whiskers from the box to the minimum (28) and maximum (57) values.

Answer:

The box - and - whisker plot has a minimum value of 28, $Q_1 = 33.5$, median $Q_2=41.5$, $Q_3 = 51.5$, and a maximum value of 57, with the box drawn from 33.5 to 51.5, a vertical line at 41.5 inside the box, and whiskers extending to 28 and 57.