(a) find the five - number summary, and (b) draw a box - and - whisker plot of the data 4 8 8 5 1 9 8 7 9 6…

Explanation:

Step1: Sort the data

1 1 2 4 4 5 6 7 7 7 8 8 8 8 9 9 9 9

Step2: Find the minimum

The minimum value (Min) of the sorted data is 1. Min = 1

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

There are $n = 18$ data points. The position of $Q_1$ is $i=\frac{n + 1}{4}=\frac{18+1}{4}=4.75$. $Q_1$ is the value between the 4th and 5th ordered data points. $Q_1=\frac{4 + 4}{2}=4$.

Step4: Find the median ($Q_2$)

The position of the median for $n = 18$ data points is $i=\frac{n+1}{2}=\frac{18 + 1}{2}=9.5$. $Q_2$ is the value between the 9th and 10th ordered data points. $Q_2=\frac{7+7}{2}=7$.

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

The position of $Q_3$ is $i=\frac{3(n + 1)}{4}=\frac{3\times(18 + 1)}{4}=14.25$. $Q_3$ is the value between the 14th and 15th ordered data points. $Q_3=\frac{8+8}{2}=8$.

Step6: Find the maximum

The maximum value (Max) of the sorted data is 9. Max = 9

Answer:

(a) Min = 1 $Q_1 = 4$ $Q_2 = 7$ $Q_3 = 8$ Max = 9 (b) Without seeing the actual box - and - whisker plots with proper scale and markings, we cannot determine the correct plot. But to draw a box - and - whisker plot:

• The left - hand side of the box is at $Q_1 = 4$.
• The line inside the box is at $Q_2=7$.
• The right - hand side of the box is at $Q_3 = 8$.
• The left whisker extends to Min = 1.
• The right whisker extends to Max = 9.