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Home » The mean of the following distribution is 50 and the sum of all the frequencies is 120. Find the values of p and q.
The mean of the following distribution is 50 and the sum of all the frequencies is 120. Find the values of p and q.
CBSE | Class 10 | Exercise 1 | Maths | Measures of Central Tendency | ML Aggarwal
The mean of the following distribution is 50 and the sum of all the frequencies is 120. Find the values of p and q.
Class intervals 0-20 20-40 40-60 60-80 80-100
Frequency 17 P 32 q 19

Solution:

Class mark, xi = (upper class limit + lower class limit)/2

Class intervals Frequency fi Class mark xi fixi
0-20 17 10 170
20-40 P 30 30P
40-60 32 50 1600
60-80 q 70 70q
80-100 19 90 1710
Total Ʃ fi = 68+P+q Ʃfixi = 3480+30P+70q

Given sum of all frequencies, Ʃ fi = 120

68+P+q = 120

P+q = 120-68 = 52

P+q = 52

P = 52-q …(i)

Given mean = 50

Mean = Ʃfixi / Ʃ fi

50 = (3480+30P+70q)/120

50×120 = 3480+30P+70q

6000 = 3480+30P+70q

6000- 3480 = 30P+70q

2520 = 30P+70q

252 = 3P+7q …(ii)

Substitute (i) in (ii)

252 = 3(52-q)+7q

252 = 156-3q+7q

252-156 = 4q

4q = 96

q = 96/4 = 24

P = 52-24 = 28

Hence the value of P and q is 28 and 24 respectively.

i

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