Finding the Mean from Graphical Representation

Here we will learn how to find the mean from graphical representation.

The ogive of the distribution of marks of 45 students is given below.

$Finding the Mean from Graphical Representation$

Find the mean of the distribution.

Solution:

The cumulative-frequency table is as given below.

Marks

Under 20

Under 40

Under 60

Under 80

Under 100

Number of Students

Writing in overlapping class intervals, the distribution is as below.

Marks

0 - 20

20 - 40

40 - 60

60 - 80

Under 100

Number of Students

The calculations are as given below.

Class Interval	Class Mark (m_i)	Frequency (f_i)	m_if_i
0 - 20	10	10	100
20 - 40	30	20	600
40 - 60	50	5	250
60 - 80	70	5	350
80 - 100	90	5	450
		$\sum f_{i}$ = 45	$\sum m_{i}f_{i}$ = 1750

Therefore, mean A = $\frac{\sum m_{i}f_{i}}{\sum f_{i}}$

= $\frac{1750}{45}$

= 38.89

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