The arithmetic mean of the following frequency distribution is 50.

Class 0-10 10-20 20-30 30-40 40-50

Frequency 16 p 30 32 14

Find the value of p.

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Solution

Class

Mid value $(x_{i})$

Frequency $(f_{i})$

$(x_{i} \times f_{i})$

0-10

5

16

80

10-20

15

$p$

15 $p$

20-30

25

30

750

30-40

35

32

1120

40-50

45

14

630

$\sum f_{i} = p + 92$

$\sum f_{i} x_{i} = 15 p + 2580$

$∴ Mean, \bar{x} = \frac{\sum f_{i} x_{i}}{\sum f_{i}} = \frac{15 p + 2580}{p + 92} Now, \frac{15 p + 2580}{p + 92} = 50 \Rightarrow 50 p + 4600 = 15 p + 2580 \Rightarrow 35 p = - 2020 \Rightarrow p = - \frac{404}{7} (frequency cannot be negative)$

So, there is an error in question.

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Similar questions

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

25

p

Class interval	$0 - 10$	$10 - 20$	$20 - 30$	$30 - 40$	$40 - 50$
Frequency	$5$	$18$	$15$	$p$	$6$

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

f_{1}

f_{2}

N = 100

32

Class	$0 - 10$	$10 - 20$	$20 - 30$	$30 - 40$	$40 - 50$	$50 - 60$	$T o t a l$
Frequency	$10$	$f_{1}$	$25$	$30$	$f_{2}$	$10$	$100$

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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