If the mean of the following frequency distribution is 54, find the value of p. [CBSE 2006C]

Class 0−20 20−40 40−60 60−80 80−100

Frequency 7 p 10 9 13

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Solution

The given data is shown as follows:

Class Frequency (f_i) Class mark (x_i) f_ix_i

0−20 7 10 70

20−40 p 30 30p

40−60 10 50 500

60−80 9 70 630

80−100 13 90 1170

Total ∑ f_i = 39 + p ∑ f_ix_i = 2370 + 30p

The mean of given data is given by

$\bar{x} = \frac{\sum_{i} f_{i} x_{i}}{\sum_{i} f_{i}} \Rightarrow 54 = \frac{2370 + 30 p}{39 + p} \Rightarrow 54 (39 + p) = 2370 + 30 p \Rightarrow 2106 + 54 p = 2370 + 30 p \Rightarrow 54 p - 30 p = 2370 - 2106 \Rightarrow 24 p = 264 \Rightarrow p = 11$

Thus, the value of p is 11.

Suggest Corrections

Class	0-10	10-20	20-30	30-40	40-50
Frequency	7	12	13	10	8

Class	50-60	60-70	70-80	80-90	90-100
Frequency	8	6	12	11	p

Class	0-20	20-40	40-60	60-80	80-100	100-120
Frequency	7	f₁	12	f₂	8	5

Class	0 – 20	20 – 40	40 – 60	60 – 80	80 – 100
Frequency	12	15	32	x	13

Class :	0−20	20−40	40−60	60−80	80−100
Frequency :	7	p	10	9	13

Classes	0−20	20−40	40−60	60−80	80−100
Frequency	17	28	32	p	19