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Question

The daily expenditure of 100 families are given below. Calculate f1 and f2 if the mean daily expenditure is ₹188.
Expenditure
(in ₹)
140−160 160−180 180−200 200−220 220−240
Number of families 5 25 f1 f2 5

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Solution

The given data is shown as follows:
Expenditure
(in ₹)
Number of families
(fi)
Class mark (xi) fixi
140−160 5 150 750
160−180 25 170 4250
180−200 f1 190 190f1
200−220 f2 210 210f2
220−240 5 230 1150
Total ∑ fi = 35 + f1 + f2 ∑ fixi = 6150 + 190f1 + 210f2

Sum of the frequencies = 100

ifi=10035+f1+f2=100f1+f2=100-35f1+f2=65f2=65-f1 ....(1)

Now, The mean of given data is given by

x¯=ifixiifi188=6150+190f1+210f210018800=6150+190f1+210f218800-6150=190f1+210f212650=190f1+21065-f1 from (1)12650=190f1-210f1+1365020f1=13650-1265020f1=1000f1=50

If f1 = 50, then f2 = 65 − 50 = 15

​Thus, the value of f1 is 50 and f2 is 15.

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