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Question 10
The mean of the following distribution is 50.

x1030507090f175a+3327a1119

Find the value of a and hence the frequencies of 30 and 70.

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Solution

We know that,
Mean of the distribution (¯x)=5i=1fixi5i=1fi=50 [given]
f1x1+f2x2+f3x3+f4x4+f5x5f1+f2+f3+f4+f5=50
(17)(10)+(5a+3)(30)+(32)(50)+(7a11)(70)+(19)(90)17+5a+3+32+7a11+19=50
170+150a+90+1600+490a770+171012a+60=50
3570770+640a12a+60=50
2800+640a=600a+3000
40a=200a=5
Frequency of 30 =5a+3=5(5)+3 [put a=5]
=25+3=28
And frequency of 70=7a11=7(5)11 [put a=5]
=3511=24
Hence, the frequencies of 30 and 70 are 28 and 24 respectively.

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