create a box - and - whisker graph with the following wages (dollars per hour): 20 10 15 9 8 5 24 29 25 18…

Explanation:

Step1: Identify the data set

The data set of wages per hour is (5,8,9,10,12,15,17,18,20,21,23,24,25,26,29,30).

Step2: Find the median (Q2)

There are (n = 16) data - points. The median is the average of the (\frac{n}{2})th and ((\frac{n}{2}+ 1))th ordered values. (\frac{n}{2}=8) and (\frac{n}{2}+1 = 9). The 8th value is (18) and the 9th value is (20), so the median (Q2=\frac{18 + 20}{2}=19).

Step3: Find Q1

The lower - half of the data set is (5,8,9,10,12,15,17,18). There are (n_1=8) data - points. The median of the lower - half (Q1) is the average of the (\frac{n_1}{2})th and ((\frac{n_1}{2}+1))th ordered values. (\frac{n_1}{2}=4) and (\frac{n_1}{2}+1 = 5). The 4th value is (10) and the 5th value is (12), so (Q1=\frac{10 + 12}{2}=11).

Step4: Find Q3

The upper - half of the data set is (20,21,23,24,25,26,29,30). There are (n_2 = 8) data - points. The median of the upper - half (Q3) is the average of the (\frac{n_2}{2})th and ((\frac{n_2}{2}+1))th ordered values. (\frac{n_2}{2}=4) and (\frac{n_2}{2}+1 = 5). The 4th value is (24) and the 5th value is (25), so (Q3=\frac{24+25}{2}=24.5).

Step5: Find Q4

The maximum value in the data set is (Q4 = 30).

Step6: Find the minimum value

The minimum value in the data set is (5).

Step7: Calculate the range

The range is (Q4 - \text{minimum value}=30 - 5=25).

Answer:

Median (=19), Q1 (=11), Q2 (=19), Q3 (=24.5), Q4 (=30), Range (=25)