Question

In the formula $x=a+h\left(\frac{\sum _i{f}_i{u}_i}{\sum _i{f}_i}\right)$ for finding the mean of grouped frequency distribution, $u_i=$

• A. $\frac{(x_i+a)}{h}$
• B. $h(x_i-a)$
• C. $\frac{(x_i-a)}{h}$
• D. $\frac{(a-x_i)}{h}$

Answer 1

The correct option is C

$\frac{(x_i-a)}{h}$

Explanation for the correct option:

Identify the mean formula:

Given, $x=a+h\left(\frac{f_i{u}_i}{f_i}\right)$

Mean is a number obtained by summing the values of a data set and dividing the sum by the total number of observation.

The formula given above is the step deviation formula for finding the mean where,
$a$ is the assumed mean.
$h$ is the width of the group.
$f_i$ is the frequency of the $i$^th class.
$u_i$ is the mean of the $i$^th class.

And, $u_i=\frac{(x_i-a)}{h}$
where, $x_i-a$ is the deviation of the $i$^th class.

Hence, option C is correct.