Question

(a) find the five - number summary, and (b) draw a box - and - whisker plot of the data. 2 8 8 3 3 9 8 7 9 6 9 2 1 6 1 9 8 7 7 9 (a) min: type your answer. q1: type your answer. q2: type your answer. q3: type your answer. max: type your answer. (b) choose the correct box - and - whisker plot below. type your answer.

Explanation:

Step1: Arrange data in ascending order

1, 1, 1, 2, 2, 3, 3, 6, 6, 7, 7, 7, 7, 8, 8, 8, 9, 9, 9, 9

Step2: Find the minimum value

Min = 1

Step3: Calculate the position of Q1

$n = 20$, position of Q1 = $\frac{n + 1}{4}=\frac{20+ 1}{4}=5.25$. So, $Q1=\frac{2 + 3}{2}=2.5$

Step4: Calculate the position of Q2 (median)

Position of Q2 = $\frac{n+1}{2}=\frac{20 + 1}{2}=10.5$. So, $Q2=\frac{7+7}{2}=7$

Step5: Calculate the position of Q3

Position of Q3 = $\frac{3(n + 1)}{4}=\frac{3\times(20 + 1)}{4}=15.75$. So, $Q3=\frac{8+8}{2}=8$

Step6: Find the maximum value

Max = 9

Answer:

Min: 1
Q1: 2.5
Q2: 7
Q3: 8
Max: 9
(Note: Since no details about the box - and - whisker plot options are clear enough to choose one, only the five - number summary is provided completely. For the box - and - whisker plot part, more information about the options is needed to give a proper answer.)