Question

Find the mean mark from the following frequency table of 100 students.

MARKS OBTAINED 30
35
40
45
50

NUMBER O STUDENTS
45
26
12
10
7​

Answer 1

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

Given data is

Let marks obtained be represented as x and number of students is represented as f.

So,

$\: \: \: \: \: \: \: \: \: \: \: \begin{gathered} \begin{array}{|c|c|} \bf{x} & \bf{f} \\ 30 & 45  \\35 & 26 \\40 & 12 \\45  & 10 \\50  & 7 \end{array}\end{gathered}$

Calculation of Mean :-

$\begin{gathered}\begin{gathered}\begin{gathered}\boxed{\begin{array}{c|c|c}\sf x&\sf \: f&\sf \:fx\\\frac{\qquad \qquad}{}&\frac{\qquad \qquad}{}&\frac{\qquad \qquad}{}\\\sf 30&\sf 45&\sf1350\\\\\sf 35&\sf 26&\sf910\\\\\sf 40 &\sf 12&\sf480\\\\\sf 45&\sf 10&\sf450 \\\\\sf 50&\sf 7&\sf350\\\frac{\qquad}{}&\frac{\qquad}{}&\frac{\qquad \qquad}{}\\\sf & \sf & \end{array}}\end{gathered}\end{gathered}\end{gathered}$

So, we have

$\rm :\longmapsto\: \sum \: fx = 3540$

$\rm :\longmapsto\: \sum \: f = 100$

Hence,

Mean using Direct Method is

$\red{\rm :\longmapsto\:Mean = \dfrac{ \sum \: fx}{ \sum \: f}}$

$\rm \: \: = \: \dfrac{3540}{100}$

$\rm \: \: = \: 35.4$

Additional Information :-

Mean using Short Cut Method

$\red{\rm :\longmapsto\:Mean =A + \dfrac{ \sum \: fd}{ \sum \: f}}$

Mean using Step Deviation Method

$\red{\rm :\longmapsto\:Mean =A + \dfrac{ \sum \: fu}{ \sum \: f} \times h}$