Question

(a) find the five - number summary, and (b) draw a box - and - whisker plot of the data. 3 8 8 6 2 9 8 7 9 6 9 5 2 6 2 9 8 7 7 9 (a) min = 2 (simplify your answer.) q1 = 5.25 (simplify your answer. do not round.) q2 = 7 (simplify your answer. do not round.) q3 = (simplify your answer. do not round.)

Explanation:

Step1: Sort the data

2 2 2 2 3 5 6 6 6 7 7 7 8 8 8 8 9 9 9 9

Step2: Find the position of Q3

There are $n = 20$ data - points. The position of $Q_3$ is $i=\frac{3(n + 1)}{4}=\frac{3\times(20 + 1)}{4}=\frac{3\times21}{4}=15.75$.

Step3: Calculate Q3

The 15th value is 8 and the 16th value is 8. Using the interpolation formula for the quartile, $Q_3=8+(8 - 8)\times0.75 = 8$.

Answer:

8