Find the missing frequencies in the following frequency distribution whose mean is 34.

x f

10 4

20 f1

30 8

40 f2

50 3

6 4

Total 35

Question

Find the missing frequencies in the following frequency distribution whose mean is 34

Accepted Answer

The average of the given numbers is computed by dividing the total number of numbers by the sum of the given numbers.

We know that

Σ fi =19 + f1 + f2

It can be written as

35 = 19 + f1 + f2

So we get

f1 + f2 = 16 …… (1)

It is given that

Mean = 34

We know that

Mean = Σ fi xi/ Σ fi

So we get

(670 + 20f1 + 40f2)/ 35 = 34

On further calculation

(335 + 10f1 + 20f2)/ 35 = 17

So we get

335 + 10f1 + 20f2 = 595

It can be written as

10f1 + 20f2 = 260

Dividing the equation by 10

f1 + 2f2 = 26 …….. (2)

By subtracting equation (1) from (2)

f2 = 10

Substituting in equation (1)

f1 + 10 = 16

So we get

f1 = 6

Therefore, the missing frequencies are 6 and 10.

RS Aggarwal Solutions Class 9 Mathematics Solutions for Mean Median And Mode Of Ungrouped Data Exercise 18B in Chapter 18 - Mean Median And Mode Of Ungrouped Data