Question

In the first proof of reading of a book containing 300 pages the following distribution of misprints was obtained:
No of misprints per page (x): 0 1 2 3 4 5
No of pages (f): 154 96 36 9 5 1

Find the average number of misprints per page.

Answer 1

ASSUMED MEAN METHOD :  

In this method, first of all, one among xi 's is chosen as the assumed mean denoted  by ‘A’. After that the difference ‘di’ between ‘A’ and each of the xi's i.e di = xi - A is calculated .  

ARITHMETIC MEAN =  A +  Σfidi / Σfi

[‘Σ’ Sigma means ‘summation’ ]

★★ We may take Assumed mean 'A’ to be that xi which lies in the middle of x1 ,x2 …..xn.

FREQUENCY DISTRIBUTION TABLE IS IN THE ATTACHMENT  

From the table : Σfidi = - 381 ,Σfi = 300  

Let the assumed mean, A = 2

ARITHMETIC MEAN =  A +  Σfidi / Σfi

ARITHMETIC MEAN =  2 + (- 381/300)

= 2 - 381/300

= 2 - 127/100

= 2 - 1 27

= 0.73

ARITHMETIC MEAN = 0.73  

Hence, the average number of misprints per page is 0.73 .  

HOPE THIS ANSWER WILL HELP YOU….

Answer 2

Answer :

The average number of misprints per page is 0.73 .

Step-by-step explanation :

Assumed mean method -

In assumed mean method, at first one of the $x_{i}$ is chosen as assumed mean which is denoted by "A".

Then we calculate the difference, $d_{i}$ by using the given formula i.e.,

$d_{i}=x_{i}-A$  

$Arithmetic\:mean=A+\frac{\Sigma f_{i}d_{i}}{\Sigma f_{i}}$

where $\Sigma$ means summation.

Let us take the assumed mean to be 2.

Frequency Distribution Table -

$\begin{tabular}{| c | c | c | c |}\cline{1-4}x_i & f_i & d_i=x_{i}-A & f_{i}d_{i} \\ \cline{1-4}0 & 154 & -2 & -308 \\ \cline{1-4}1 & 95 & -1 & -95 \\ \cline{1-4}2 & 36 & 0 & 0 \\ \cline{1-4}3 & 9 & 1 & 9 \\ \cline{1-4}4 & 5 & 2 & 10 \\ \cline{1-4}5 & 1 & 3 & 3 \\ \cline{1-4} & \Sigma f_{i}=300 & & \Sigma f_{i}d_{i}=-381\\ \cline{1-4}\end{tabular}$

Since, Arithmetic mean -

$\implies A+\frac{\Sigma f_{i}d_{i}}{\Sigma f_{i}}$

$\implies 2+\frac{(-381)}{300}$

$\implies 2-\frac{381}{300}$

$\implies 2-\frac{127}{100}$

$\implies 2-1.27$

$\implies 0.73$