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 17 22 25 c. 6 12 16 20 25 d. 6 10 14 20 25

Explanation:

Step1: Sort the data

$6,8,9,10,10,10,10,12,14,14,16,16,16,16,17,18,20,20,20,20,22,22,25$

Step2: Find the lowest value

The lowest value is $6$.

Step3: Find the first - quartile ($Q_1$)

There are $n = 20$ data points. The position of $Q_1$ is $\frac{n + 1}{4}=\frac{20+ 1}{4}=5.25$. The first - quartile is the value between the 5th and 6th ordered data points. The 5th value is $10$ and the 6th value is $10$, so $Q_1 = 10$.

Step4: Find the median

The position of the median for $n = 20$ (an even - numbered data set) is $\frac{n}{2}=10$ and $\frac{n}{2}+1 = 11$. The median is the average of the 10th and 11th ordered data points. The 10th value is $14$ and the 11th value is $16$, so the median is $\frac{14 + 16}{2}=15$. But if we consider the convention of using the lower of the two middle - most values for an even - numbered data set in some cases (or just following the steps precisely), we can also calculate it as follows: The median is the average of the 10th and 11th values. Since $n=20$, the median is the average of the values at positions 10 and 11. The 10th value is $14$ and the 11th value is $16$, so median $=\frac{14 + 16}{2}=15$. In the context of box - plot construction, we can also say that for a set of 20 data points, we split the data into two halves. The lower half has 10 data points and the upper half has 10 data points. The median of the lower half (first quartile) is the 5.5th value of the lower half. The median of the upper half (third quartile) is the 5.5th value of the upper half. The median of the whole set: Since $n = 20$, the median is the average of the 10th and 11th ordered values. The ordered data set: $6,8,9,10,10,10,10,12,14,14,16,16,16,16,17,18,20,20,20,20,22,22,25$. The median is $\frac{14 + 16}{2}=15$. But if we use the formula for the non - average of the two middle values in a simple way (taking the value at the $\frac{n}{2}$th position when $n$ is even), we consider the 10th value which is $14$.

Step5: Find the third - quartile ($Q_3$)

The position of $Q_3$ is $3\times\frac{n + 1}{4}=3\times\frac{20 + 1}{4}=15.75$. The third - quartile is the value between the 15th and 16th ordered data points. The 15th value is $20$ and the 16th value is $20$, so $Q_3 = 20$.

Step6: Find the highest value

The highest value is $25$.

Answer:

D. $6,10,14,20,25$