Mean of five consecutive even numbers is 16, find the variance of the numbers.

Question

Question

Answer 1

Given:

Mean of five consecutive even numbers = 16

Formula used:

V = variance

∑ = summation

x = observation

n = number of observations

a = 1^st term of the numbers

d = common difference

Calculation:

⇒ 2a + (5 – 1)2 = 32

⇒ 2a + 4 × 2 = 32

⇒ 2a = 32 – 8

⇒ 2a = 24

⇒ a = 12

1^stterm = 12

Other terms are 14, 16, 18, 20

⇒

⇒ 8

⇒ V = 8

∴ The variance of the numbers is 8

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