Chapter 2.2, Problem 2.45E

(a)

To determine

To Explain: the five-number summary on the basis of given distribution.

Answer to Problem 2.45E

3,4,8,13,55

Explanation of Solution

Given:

  

By seeing the stem-leaf plot minimum and maximum values are 3 and 55 respectively so the spread of the data will be 3 to 55. The 1^st quartile and 3^rd quartile are 4 and 13 respectively. The median is 8 which is the middle value of the sorted data set. Therefore five number summaries are then 3, 4,8,13 and 55.

(b)

To determine

To Explain: the outlier if it is there, explain it with calculation

Answer to Problem 2.45E

Explanation of Solution

Given:

  

Formula used:

  ${\text{IQR=Q}}_3-Q_1$

  ${\text{Q}}_3+1.5\left(\text{IQR}\right)$

  ${\text{Q}}_1-1.5\left(\text{IQR}\right)$

Calculation:

  $\begin{array}{c}{\text{IQR=Q}}_3-Q_1\\ =13-4\\ =9\\ {\text{Q}}_3+1.5\left(\text{IQR}\right)=13+1.5\left(9\right)\\ =26.5\\ {\text{Q}}_1-1.5\left(\text{IQR}\right)=4+1.5\left(9\right)\\ =-9.5\end{array}$

By seeing the stem plot and the calculation it indicates that there are 4 outliers which is 27,31,34,55 because all the larger than 26.5 and inter quartile range is the difference of the third and first quartile which is 9 which shows that spread of the middle half or middle 50% of the data.

(c)

To determine

To construct: the box plot on the basis of given data.

Explanation of Solution

Given:

  

Graph:

  

By seeing the box plot and the calculation it indicates that there are 4 outliers which is 27,31,34,55 because all the larger than 26.5 and one of them is extreme outlier. Inter quartile range is the difference of the third and first quartile which is 9 and median is about 8.