In the first proof reading of a book containing 300 pages the following distribution of misprints was obtained:
No .of misprints per pages ($x$): 0 1 2 3 4 5
No. of pages ($f$): 154 95 36 9 5 1
Find the average number of misprints per page.

Given:

In the first proof reading of a book containing 300 pages, the given distribution of misprints was obtained.

To do:

We have to find the average number of misprints per page.

Solution:

Let the assumed mean be $A=2$

Number of misprints per page ($x_i$)	Number of pages ($f_i$)	$d_i = x_i -A$	$f_i \times\ d_i$
0	154	$-2$	$-308$
1	95	$-1$	$-95$
2-$A$	36	0	0
3	9	1	9
4	5	2	10
5	1	3	3
Total	$\sum{f_i}=300$		$\sum{f_id_i}=-381$

We know that,

Mean $=A+\frac{\sum{f_id_i}}{\sum{f_i}}$

Therefore,

Mean $=2+\frac{-381}{300}$

$=2-1.27$

$=0.73$

The average number of misprints per page is $0.73$.

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Updated on: 10-Oct-2022

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No .of misprints per pages ($x$):	0	1	2	3	4	5
No. of pages ($f$):	154	95	36	9	5	1

In the first proof reading of a book containing 300 pages the following distribution of misprints was obtained:No .of misprints per pages ($x$):012345No. of pages ($f$):1549536951Find the average number of misprints per page.