The arithmetic mean of the following frequency distribution is $25$ . Determine value of $p$ .
Class interval $0 - 10$ $10 - 20$ $20 - 30$ $30 - 40$ $40 - 50$
Frequency $5$ $18$
$15$ $p$ $6$

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Solution

Given Arithmetic mean $= 25$
Arithmetic mean Formula $= \frac{s u m o f f r e q u e n c y}{N o . o f o b s e r v a t i o n}$
$25 = \frac{5 + 18 + 15 + P + 6}{5}$
$125 = 44 + P$
$P = 125 - 44$
$P = 81$
$∴$ value of $P = 81$

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Class	0-10	10-20	20-30	30-40	40-50
Frequency	16	p	30	32	14

Class-interval	$0 - 10$	$10 - 20$	$20 - 30$	$30 - 40$	$40 - 50$	$50 - 60$
Frequency	$7$	$14$	$28$	$26$	$16$	$9$

31.4

x

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

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

Class interval	0-50	50-100	100-150	150-200	200-250	250-300
Frequency	17	35	43	40	21	24

Class	0-10	10-20	20-30	30-40	40-50
Frequency	15	20	35	p	10

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