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If the mean of the following distribution is 27, then the value of p is ____.

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

see full answer

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Detailed Solution

If the mean of the following distribution is 27, then the value of p is 7.
Given:

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

Mean = ∑ f i x i ∑ f i

The mean of the data is 27. We have to find the value of p. The frequency distribution table of the given data for set:

Class	Frequency, fi	Mid-value, xi	fixi
0-10	8	5	40
10-20	P	15	15p
20-30	12	25	300
30-40	13	35	455
40-50	10	45	450
	Σfi=43+p		Σfixi=1245+15p

To calculate the value of p, we will apply the formula of mean:

27 = 1245 + 15 p 43 + p 1161 + 27 p = 1245 + 15 p 27 p − 15 p = 1245 − 1161 12 p = 84 p = 7

Thus, the value of p is 7.

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