Question

Consider a grouped data distribution for which the mean is found by assumed mean method.

P = sum of the products of ‘d’ and frequency for each class interval

Here $d_i=x_i-A$

Q = total number of observations

A = assumed mean

M = mean of given grouped data distribution

Which of the following statements is true?

• A. $M=A+\frac{Q}{P}$
• B. $M=A+\frac{P}{Q}$
• C. $M=P+\frac{A}{Q}$
• D. $M=Q+\frac{A}{P}$

Answer 1

The correct option is B $M=A+\frac{P}{Q}$

Here we can write:

$M=A+\frac{\sum f_i{d}_i}{\sum f_i}$
Given:
$\sum f_i{d}_i=P$
$\sum f_i=Q$
Where,
$f_i=$ frequency of $i^{th}$ class

$d_i=x_i–A$

$x_i=i^{th}$ class mark

$A=$ assumed mean

$\therefore M=A+\frac{P}{Q}$