Chapter 1.3, Problem 96E

(a)

To determine

To calculate the median of the given data.

Answer to Problem 96E

Median = 4

Explanation of Solution

Given:

  

Calculation:

X	f	$cf$
1	5	5
2	12	17
3	22	39
4	23	62
5	12	74
6	7	81
7	5	86
8	4	90
9	3	93
10	2	95

  $\begin{array}{l}\text{Median = }{\left(\frac{n+1}{2}\right)}^{\text{Th term}}\\ ={\left(\frac{95+1}{2}\right)}^{\text{Th term}}\\ ={48}^{\text{Th term}}\\ \text{Since the cf 48 falls less than 62,}\\ \text{Which means that Median is 4}\text{.}\end{array}$

(b)

To determine

To calculate the mean of the given graph.

Answer to Problem 96E

Mean = 4.24

Explanation of Solution

Formula used:

  $\text{Mean = }\frac{\sum fx}{\sum f}$

Calculation:

X	f	$fx$
1	5	5
2	12	24
3	22	66
4	23	92
5	12	60
6	7	42
7	5	35
8	4	32
9	3	27
10	2	20

  $\begin{array}{c}\text{Mean = }\frac{\sum fx}{\sum f}\\ =\frac{403}{95}\\ =4.24\end{array}$