Question

the data set 5, 6, 7, 8, 9, 9, 9, 10, 12, 14, 17, 17, 18, 19, 19 represents the number of hours spent on the internet in a week by students in a mathematics class. which box - and - whisker plot represents the data? 1) box - and - whisker plot image with number line from 2 to 20 2) box - and - whisker plot image with number line from 2 to 20 3) box - and - whisker plot image with number line from 2 to 20 4) box - and - whisker plot image with number line from 2 to 20

Explanation:

Step1: Find the minimum value

The minimum value of the data - set 5, 6, 7, 8, 9, 9, 9, 10, 12, 14, 17, 17, 18, 19, 19 is 5.

Step2: Find the first - quartile ($Q_1$)

There are $n = 15$ data points. The position of $Q_1$ is $\frac{n + 1}{4}=\frac{15+1}{4}=4$. So, $Q_1$ is the 4th ordered data - point, which is 8.

Step3: Find the median ($Q_2$)

The position of the median is $\frac{n + 1}{2}=\frac{15 + 1}{2}=8$. So, the median $Q_2$ is 10.

Step4: Find the third - quartile ($Q_3$)

The position of $Q_3$ is $\frac{3(n + 1)}{4}=\frac{3\times(15 + 1)}{4}=12$. So, $Q_3$ is 17.

Step5: Find the maximum value

The maximum value of the data - set is 19.

A box - and - whisker plot has the minimum value at the end of the left - most whisker, $Q_1$ at the left - hand side of the box, the median at the line inside the box, $Q_3$ at the right - hand side of the box, and the maximum value at the end of the right - most whisker.

The box - and - whisker plot should have the left - most whisker starting at 5, the left side of the box at 8, the line in the box at 10, the right side of the box at 17, and the right - most whisker ending at 19.

Answer:

4)