If the mean of the following data is 20.2, find the value of p:
x 10 15 20 25 30
f 6 8 p 10 6

Solution:

Given, the mean of the given data is 20.2

We have to find the value of p.

Mean of ungrouped data = Mean = ∑fx / ∑f

Where, f are the frequencies of x

Mean = [(10 × 6) + (15 × 8) + (20 × p) + (25 × 10) + (30 × 6)] / (6 + 8 + p + 10 + 6)

So, 20.2 = [60 + 120 + 20p + 250 +180] / (14 +p +16)

20.2 = [180 + 180 + 250 + 20p] / (30 + p)

20.2(30 + p) = 360 + 250 + 20p

606 + 20.2p = 610 + 20p

On rearranging,

20.2p - 20p = 610 - 606

0.2p = 4

p = 4/0.2

p = 20

Therefore, the value of p is 20.

✦ Try This: If the mean of the following data is 24, find the value of p:

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

NCERT Exemplar Class 9 Maths Exercise 14.3 Problem 9

If the mean of the following data is 20.2, find the value of p: x 10 15 20 25 30 f 6 8 p 10 6

Summary:

The mean of the given data is 20.2. The value of p is 20

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