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Question

The mean of the following frequency table is 50. Find the values of x and y.
Class-interval02020404060608080100Total
Frequency17x32y19120

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Solution

Let the assumed mean be A=50 and h=20
Table for step deviation is given:

Class IntervalFrequency, fi Mid Value ui=xiAh fiui
02017 10 2 34
2040x 30 1 x
406032 50 0 0
6080y 70 1 y
8010019 90 2 38
Total 68+x+y 4x+y
We have N=fi=120
68+x+y=120
x+y=52 ... (i)
Mean =50
Mean =A+(1Nfiui)h
50=50+(1120×(4x+y))×20
xy=4 ... (ii)
From (i) and (ii), we get
x=28,y=24

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