Question

2) The mean of the following frequency distribution is 50 and the sum of all the frequencies is
120. Find the missing frequencies x and y.
Classes
0 - 20 20 - 40 40 - 60 60 - 80 80 – 100 Total
Frequencies 17
у
19
120
x
32​

Answer 1

Answer:

The value of f1 and f2 are 28 and 24.

Solution:

The sum of the frequency is equal to 120, so the sum be 17+f1+32+f2+19 = 120,

which means the sum of f1+f2 = 120 – 68

f1 + f2 = 52.

Now for the mean of the frequency we can say that 50=\frac{\sum f_{i} x_{i}}{\Sigma f_{i}}50=

Σf

i

∑f

i

x

i

that means

The sum off_{i} x_{i}f

i

x

i

is equal to \frac{3480+30 f 1+70 f 2}{120}

120

3480+30f1+70f2

50=\frac{3480+30 f 1+70 f 2}{120}=

120

3480+30f1+70f2

we get the another equation for f1 and f2 i.e. 2520=30f1+70f2

Now equating 2520=30 f1+70 f2 and f1 + f2 = 52.

We get the value of f1 as 28 and f2 as 24.

Therefore, the value of f1 and f2 is equal to 28 and 24 respectively.