Question

select the correct answer.
the table shows the number of hours hazel worked per week at her part - time job for the last 20 weeks.
9 22 16 12 16 10 22 16 17 8
20 18 10 20 25 6 14 10 14 20
identify the five number summary (lowest value, first quartile, median, third quartile, and highest value) for the corresponding box plot.
○ a. 6, 12, 18, 22, 25
○ b. 6, 10, 16, 20, 25
○ c. 6, 12, 16, 20, 25
○ d. 6, 10, 17, 22, 25

Explanation:

Step1: Sort the data

First, sort the data set: \(6,8,9,10,10,10,12,14,14,16,16,16,17,18,20,20,20,22,22,25\)

Step2: Find the lowest and highest values

The lowest value is \(6\), and the highest value is \(25\).

Step3: Find the median

Since \(n = 20\) (even), the median is the average of the \(\frac{n}{2}=10\)th and \(\frac{n}{2}+1 = 11\)th values. The \(10\)th value is \(16\), and the \(11\)th value is \(16\). So, the median \(M=\frac{16 + 16}{2}=16\)

Step4: Find the first quartile

The first quartile \(Q_1\) is the median of the lower half. The lower half is \(6,8,9,10,10,10,12,14,14,16\). Since \(n_1=10\) (even), \(Q_1=\frac{10+10}{2} = 10\)

Step5: Find the third quartile

The third quartile \(Q_3\) is the median of the upper half. The upper half is \(16,17,18,20,20,20,22,22,25\). Since \(n_3 = 10\) (even), \(Q_3=\frac{20+20}{2}=20\)

Answer:

B. \(6,10,16,20,25\)