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Home » The mean of the following frequency distribution is 57.6 and the sum of all the frequencies is 50. Find the values of p and q.
The mean of the following frequency distribution is 57.6 and the sum of all the frequencies is 50. Find the values of p and q.
CBSE | Class 10 | Exercise 1 | Maths | Measures of Central Tendency | ML Aggarwal
The mean of the following frequency distribution is 57.6 and the sum of all the frequencies is 50. Find the values of p and q.
Class intervals 0-20 20-40 40-60 60-80 80-100 100-120
Frequency 7 P 12 q 8 5

Solution:

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

Class intervals Frequency fi Class mark xi fixi
0-20 7 10 70
20-40 P 30 30P
40-60 12 50 600
60-80 q 70 70q
80-100 8 90 720
100-120 5 110 550
Total Ʃ fi = 32+P+q Ʃfixi = 1940+30P+70q

Given sum of all frequencies, Ʃ fi = 50

32+P+q = 50

P+q = 50-32= 18

P+q = 18

P = 18-q …(i)

Given mean = 57.6

Mean = Ʃfixi / Ʃ fi

57.6 = (1940+30P+70q)/50

57.6 ×50 = 1940+30P+70q

2880= 1940+30P+70q

2880- 1940 = 30P+70q

940 = 30P+70q

94 = 3P+7q …(ii)

Substitute (i) in (ii)

94 = 3(18-q)+7q

94 = 54-3q+7q

94-54= 4q

40 = 4q

q = 40/4 = 10

P = 18-10 = 8

Hence the value of P and q is 8 and 10 respectively.

i

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