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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.

Solution:

Given, the mean of the following distribution is 50.

We have to find the value of a and the frequencies of 30 and 70.

We know that, Mean of ungrouped data = Mean = ∑fx / ∑f

Where, f are the frequencies of x

So, mean = [(17 × 10) + [(5a + 3) × 30] + (32 × 50) + [(7a - 11) × 70] + (19 × 90)] / (17 + 5a + 3 + 32 + 7a - 11 + 19)

50 = [170 + 150a + 90 + 1600 + 490a - 770 + 1710] / (12a + 60)

50 = (3570 - 770 + 640a)/(12a + 60)

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

600 a + 3000 = 2800 + 640a

640a - 600a = 3000 - 2800

40a = 200

a = 200/40

a = 20/4

a = 5

Therefore, the value of a is 5

Frequency of 30 = 5a + 3

= 5(5) + 3

= 25 + 3

= 28

Frequency of 70 = 7a - 11

= 7(5) - 11

= 35 -11

= 24

Therefore, the frequencies of 30 and 70 are 28 and 24.

✦ Try This: The mean of the following distribution is 50.

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

☛ Also Check: NCERT Solutions for Class 9 Maths Chapter 14

NCERT Exemplar Class 9 Maths Exercise 14.4 Problem 10

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.

Summary:

The mean of the following distribution is 50. The value of a is 5 and hence the frequencies of 30 and 70 are 28 and 24 respectively

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