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.

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

10

30

35

40

45

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

Marks

0 - 20

20 - 40

40 - 60

60 - 80

Under 100

Number of Students

10

20

5

5

5

The calculations are as given below.

 Class Interval Class Mark (mi) Frequency (fi) mifi 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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