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

Class

0-10

10-20

20-30

30-40

40-50

Frequency

8

p

12

13

10

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Solution

Cls x
Mid pt f
frequency xf

0 - 10 5 8 40

10 -20 15 P 15P
20 - 30 25 12 300
30 - 40 35 13 445
40 -50 45 10 450
$\sum f = 43 + P$ $\sum f x = 1245 + 15 P$
Given mean = 27
we know that $\frac{\sum f x}{\sum f} = 27$

$\Rightarrow \frac{1245 + 15 P}{43 + P} = 27$
$\Rightarrow 1245 + 15 P = 27 (43 + P)$
$\Rightarrow 1245 + 15 P = 1161 + 27 P$
$\Rightarrow 1245 - 1161 = 27 P - 15 P$

$\Rightarrow 84 = 12 P$

$\Rightarrow P = \frac{84}{12} = 7$

$∴ P = 7$

Suggest Corrections

Class	$0 - 10$	$10 - 20$	$20 - 30$	$30 - 40$	$40 - 50$	$50 - 60$
Frequency	$5$	$x$	$10$	$12$	$7$	$8$

Class:	0−10	10−20	20−30	30−40	40−50
Frequency:	8	p	12	13	10

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