Chapter 4, Problem 14E

(a)

To determine

To find: the median.

Answer to Problem 14E

13.5

Explanation of Solution

Given:

25, 19, 9, 16, 3, 21, 7, 17, 10, 4, 18, 17, 4, 12, 17, 5, 10, 29, 22, 36, 19, 32, 4, 45, 1, 13, 35, 17, 23, 10, 14, 7, 15, 7, 27, 3, 27, 3, 3, 11, 12, 3

Calculation:

Total number of sample =42

Median is the average of the two values in the position

  $\frac{n}{2}=21and\frac{n}{2}+1=22$

Therefore

  $\frac{13+14}{2}=13.5$

Median is 13.5

(b)

To determine

To find: the quartiles.

Answer to Problem 14E

Explanation of Solution

Given:

25, 19, 9, 16, 3, 21, 7, 17, 10, 4, 18, 17, 4, 12, 17, 5, 10, 29, 22, 36, 19, 32, 4, 45, 1, 13, 35, 17, 23, 10, 14, 7, 15, 7, 27, 3, 27, 3, 3, 11, 12, 3

Formula used:

  ${\text{Q}}_1=1\times \left(\frac{\text{N+1}}{4}\right)\text{th postion}$

  ${\text{Q}}_3=3\times \left(\frac{\text{N+1}}{4}\right)\text{th postion}$

Calculation:

Total number of sample = 42

  $\begin{array}{c}{\text{Q}}_1=1\times \left(\frac{\text{N+1}}{4}\right)\text{th postion}\\ =1\times \left(\frac{\text{42+1}}{4}\right)\text{th postion}\\ \text{=10}\text{.75}\\ \text{=10th position +0}\text{.75}\left(11th-10th\right)\\ =5+0.75\left(7-5\right)\\ =6.5\end{array}$

  $\begin{array}{c}{\text{Q}}_3=3\times \left(\frac{\text{N+1}}{4}\right)\text{th postion}\\ =3\times \left(\frac{\text{42+1}}{4}\right)\text{th postion}\\ \text{=32}\text{.25}\\ \text{=32th position+0}\text{.25}\left(33th-32th\right)\\ =21+0.25\left(22-21\right)\\ =21.50\end{array}$

Therefore the 1^st quartile and 3^rd quartile are 6.5 and 21.5 respectively.

(c)

To determine

To Explain: based on the 5-number summary.

Explanation of Solution

Given:

25, 19, 9, 16, 3, 21, 7, 17, 10, 4, 18, 17, 4, 12, 17, 5, 10, 29, 22, 36, 19, 32, 4, 45, 1, 13, 35, 17, 23, 10, 14, 7, 15, 7, 27, 3, 27, 3, 3, 11, 12, 3

In the super ball games, generally 13.5 points in the total number of scored by both the teams. Arranging the scores in first in the ascending order then middle half of the scores is lied between 6.5 and 21.5 points. 45 points scores in the 42 matches only one time.