If the mean of the following distribution is 54, find the value of p:

Class : 0−20 20−40 40−60 60−80 80−100

Frequency : 7 p 10 9 13

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Solution

Consider the table given below:

Class Interval Frequency(f_i) Class Mark(x_i) f_i x_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

$\sum_{}^{} f_{i} = 39 + p$ $\sum_{}^{} f_{i} x_{i} = 2370 + 30 p$

It given that the mean of the distribution is 54.

$∴ Mean = \frac{\sum_{}^{} f_{i} x_{i}}{\sum_{}^{} f_{i}} \Rightarrow \frac{2370 + 30 p}{39 + p} = 54 \Rightarrow 2370 + 30 p = 2106 + 54 p \Rightarrow 54 p - 30 p = 2370 - 2106$

$\Rightarrow 24 p = 264 \Rightarrow p = \frac{264}{24} = 11$

Hence, 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
Frequency	12	15	32	x	13

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 :	7	p	10	9	13

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