The mean of five observations is 4 and their variance is 2.8 . If three of these observations are 2 , 2 and 5 , then the other two are

Question

The mean of five observations is 4 and their variance is 2.8 . If three of these observations are 2 , 2 and 5 , then the other two are, 2 and 9, 3 and 8, 4 and 7, 5 and 6

MARKS App · Accepted Answer

x ¯ = 4 , N = 5 and Σ x - x ¯ 2 N = 2.8 ⇒ Σ x - x ¯ 2 = 2.8 5 ∴ Σ x - x ¯ 2 = 1 4 ∴ 2 - 4 2 + 2 - 4 2 + 5 - 4 2 + α - 4 2 + β - 4 2 = 1 4 Where α , β are the other two observations. ∴ 4 + 4 + 1 + α - 4 2 + β - 4 2 = 1 4 ∴ α - 4 2 + β - 4 2 = 5 Also, 2 + 2 + 5 + α + β 5 = 4 ∴ α + β = 20 - 9 = 1 1 Clearly 5 , 6 only satisfy the above equations in α , β . Hence, the required numbers are 5,6 .

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