Chapter 4, Problem 13E

(a)

To determine

To find: the median.

Answer to Problem 13E

45

Explanation of Solution

Given:

45, 47, 23, 30, 29, 27, 21, 31, 22, 38, 46, 37, 66, 50, 37, 47, 44, 47, 54, 56, 59, 52, 36, 65, 39, 61, 69, 43, 75, 44, 56, 55, 53, 39, 41, 37, 69, 61, 45, 31, 46, 31

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

  $\frac{45+45}{2}=45$

Median is 45.

(b)

To determine

To find: the quartiles.

Answer to Problem 13E

Therefore the 1^st quartile and 3^rd quartile are 36.72 and 55.25 respectively.

Explanation of Solution

Given:

45, 47, 23, 30, 29, 27, 21, 31, 22, 38, 46, 37, 66, 50, 37, 47, 44, 47, 54, 56, 59, 52, 36, 65, 39, 61, 69, 43, 75, 44, 56, 55, 53, 39, 41, 37, 69, 61, 45, 31, 46, 31

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

  $\begin{array}{c}{\text{Q}}_1=1\times \left(\frac{\text{N+1}}{4}\right)\text{th postion}\\ =1\times \left(\frac{\text{42+1}}{4}\right)\text{th postion}\\ \text{=10}\text{.75}\\ \text{=10th position +0}\text{.75}\left(11th-10th\right)\\ =36+0.75\left(37-36\right)\\ =36.75\end{array}$

  $\begin{array}{c}{\text{Q}}_3=3\times \left(\frac{\text{N+1}}{4}\right)\text{th postion}\\ =3\times \left(\frac{\text{42+1}}{4}\right)\text{th postion}\\ \text{=32}\text{.25}\\ \text{=32th position+0}\text{.25}\left(33th-32th\right)\\ =55+0.25\left(56-55\right)\\ =55.25\end{array}$

Therefore the 1^st quartile and 3^rd quartile are 36.72 and 55.25 respectively.

(c)

To determine

To Explain: the description based on the 5 number summaries.

Explanation of Solution

Given:

45, 47, 23, 30, 29, 27, 21, 31, 22, 38, 46, 37, 66, 50, 37, 47, 44, 47, 54, 56, 59, 52, 36, 65, 39, 61, 69, 43, 75, 44, 56, 55, 53, 39, 41, 37, 69, 61, 45, 31, 46, 31

In the super ball games, 45 points scored by both the team generally. Arranging the data in the ascending order then middle half of the scores lie between about 37 and 55 points and some games team scored point near 27 and in the 75 points scored in the 42 matches only one time.