 # 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

Question 14 Mean Median And Mode Of Ungrouped Data Exercise 18B

The mean of the following distribution is 50.

x f
10 17
30 5a+3
50 32
70 7a-11
90 19

Find the value of a and hence the frequencies of 30 and 70.

x f xifi
10 17 170
30 5a+3 150a + 90
50 32 1600
70 7a-11 490a - 770
90 19 171
Total Σ fi = 60 + 12a Σ fi xi = 2800 + 640a

It is given that

Mean = 50

We know that

Mean = Σ fi xi/ Σ fi

So we get

(2800 + 640a)/ (60 + 12a) = 50

On further calculation

2800 + 640a = 3000 + 600a

So we get

40a = 200

By division

a = 5

We know that

Frequency of 30 = 5a + 3

By substituting the values

Frequency of 30 = 5 (5) + 3

So we get

Frequency of 30 = 28

We know that

Frequency of 70 = 7a - 11

By substituting the values

Frequency of 70 = 7 (5) - 11

So we get

Frequency of 70 = 24

Therefore, the value of a is 5 and the frequencies of 30 and 70 is 28 and 24.

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