Question

Find the mean of the following grouped frequency distribution by using any method:
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Answer 1

$\large\underline{\sf{Solution-}}$

Given data is

$\begin{gathered} \begin{array}{|c|c|} \bf{Marks} & \bf{number \: of \: students} \\ 10 - 20 & 2  \\20 - 30 & 4 \\30 - 40 & 7 \\40 - 50 & 6 \\50 - 60 & 1 \end{array}\end{gathered}$

Now, we evaluate Mean by using Direct Method.

The distribution table is as follow :-

$\begin{gathered} \begin{array}{|c|c|c|c|} \bf{Marks} & \bf{number \: of \: students \: f_i}& \bf{x_i}& \bf{f_i \: x_i} \\ 10 - 20 & 2 & 15& 30 \\20 - 30 & 4 & 25& 100\\30 - 40 & 7 & 35& 245\\40 - 50 & 6 & 45& 270\\50 - 60 & 1 & 55& 55\end{array}\end{gathered}$

So, we get

$\rm :\longmapsto\: \sum \: f_i = 20$

$\rm :\longmapsto\: \sum \: f_i \: x_i= 700$

So, Mean using Direct Method,

$\rm :\longmapsto\:Mean \: = \: \dfrac{ \sum \: f_i \: x_i}{ \sum \: f_i}$

$\rm \: \: = \: \dfrac{700}{20}$

$\rm \: \: = \: 35$

Hence,

$\bf :\longmapsto\:Mean \: = \: 35$

Additional Information :-

1. Mean using Short Cut Method

$\rm :\longmapsto\:Mean \: = \:A \: + \: \dfrac{ \sum \: f_i \: d_i}{ \sum \: f_i}$

2. Mean using Step Deviation Method

$\rm :\longmapsto\:Mean \: = \:A \: + \: \dfrac{ \sum \: f_i \: u_i}{ \sum \: f_i} \times h$