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Question 70

Let the mean and the variance of 6 observations $$a, b, 68, 44, 48, 60$$ be 55 and 194, respectively. If $$a > b$$, then $$a + 3b$$ is

Solution

Mean=55

(a+b+68+44+48+60)/6=55.

a+b=330-220=110.

Variance=194: Σ(xᵢ-55)²/6=194. Σ(xᵢ-55)²=1164.

(a-55)²+(b-55)²+(68-55)²+(44-55)²+(48-55)²+(60-55)²=1164.

(a-55)²+(b-55)²+169+121+49+25=1164. (a-55)²+(b-55)²=800.

Let a-55=p, b-55=q. p+q=110-110=0, so q=-p. p²+p²=800, p²=400, p=±20.

a>b: a=75, b=35. a+3b=75+105=180.

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