Find the mean and variance for the first 10 multiples of 3

Solution:

The first ten multiples of 3 are 3, 6, 9, 12, 15, 18, 21, 24, 27, 30

Here, the number of observations, n = 10

Mean of the data

x = (∑¹⁰_{i = 1}x_i)/10

= 165/10

= 16.5

The following table is obtained for the first 10 multiples of 3

xi	(xi - x)	(xi - x)²
3	- 13.5	182.25
6	- 10.5	110.25
9	- 7.5	56.25
12	- 4.5	20.25
15	- 1.5	2.25
18	1.5	2.25
21	4.5	20.25
24	7.5	56.25
27	10.5	110.25
30	13.5	182.25
		742.5

The variance of the data

(σ²) = 1/n ∑¹⁰_{i = 1}(x_i - x)²

= 1/10 × 742.5

= 74.25

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NCERT Solutions Class 11 Maths Chapter 15 Exercise 15.2 Question 3

Find the mean and variance for the first 10 multiples of 3

Summary:

The mean and variance for the first 10 multiples of 3 are 16.5 and 74.25