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Question

Find the missing frequencies in the following distribution , if the sum of the frequencies is 120 and the mean is 50.

Class02020404060608080100Frequency17f132f219

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Solution

It is given that mean of the data is 50 and N=120

Let the assumed mean A=50 and h=10.

MarksMid values (xi)Frequencyui=xi50Afiui0201017234204030f11f14060503200608070f21f2801009019238N=68+f1+f2fiui=4f1+f2

From the table, N=68+f1+f2, fiui=4f1+f2 and ¯x=50

68+f1+f2=120

f1+f2=12068

f1+f2=52---(1)

Mean in short-cut method,

(¯x)=A+(fiuiN)×h

50=50+(4f1+f2N)×h

5050=(4f1+f2N)×h

0=4f1+f2

f1f2=4---(2)

add (1) and (2)

f1+f2+f1f2=52+4

2f1=56

f1=28---(3)

From f1+f2=64

28+f2=52

f2=5228

f2=24---(4)


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