the ages of the n = 21 employees at a small retail store are displayed in the following stem - and - leaf…

Explanation:

Step1: Write out all data values

The data values from the stem - and - leaf plot are: 20, 20, 21, 21, 26, 29, 30, 31, 32, 38, 39, 45, 47, 51, 54, 54, 54, 57, 61, 67. There are (n = 21) data points.

Step2: Find the median (med)

For a set of (n = 21) (odd number of) data points, the median is the (\left(\frac{n + 1}{2}\right))-th value. (\frac{21+1}{2}=11) - th value. Arranging the data in ascending order, the 11 - th value is 39. So, (med = 39).

Step3: Find the lower half for (Q_1)

The lower half of the data consists of the first 10 values: 20, 20, 21, 21, 26, 29, 30, 31, 32, 38. Since (n_1=10) (even number of) data points, the median of the lower half ((Q_1)) is the average of the (\frac{n_1}{2})-th and (\left(\frac{n_1}{2}+1\right))-th values. (\frac{10}{2}=5) and (\frac{10}{2}+1 = 6). The 5 - th value is 26 and the 6 - th value is 29. So, (Q_1=\frac{26 + 29}{2}=27.5).

Step4: Find the upper half for (Q_3)

The upper half of the data consists of the last 10 values: 45, 47, 51, 54, 54, 54, 57, 61, 67. Since (n_2 = 10) (even number of) data points, the median of the upper half ((Q_3)) is the average of the (\frac{n_2}{2})-th and (\left(\frac{n_2}{2}+1\right))-th values. (\frac{10}{2}=5) and (\frac{10}{2}+1=6). The 5 - th value is 54 and the 6 - th value is 54. So, (Q_3 = 54).

Answer:

(Q_1 = 27.5), (med=39), (Q_3 = 54)