Question

create a box - and - whisker graph with the following wages (dollars per hour): 20 10 15 9 8 5 24 29 25 18 17 12 26 23 21. median (middle number) = _. quartile #1 = _. quartile #2 = _. quartile #3 = _. quartile #4 = _. range (biggest - smallest) = _

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 \(=25\)