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Seven observations have mean 8 and variance 16. Five of them are 2, 4, 10, 12 and 14. What are the other two?

Competition practiceStatistics

A6 and 8
B4 and 10
C5 and 9
D7 and 7

Step-by-Step Solution

Sum

= 56 \Rightarrow a + b = 56 - 42 = 14.Σ x^{2} = 7 (16 + 64) = 560

; the five known squares add to 460, so

a^{2} + b^{2} = 100

. With

a + b = 14 : ab = 48

, giving 6 and 8.

Answer: A) 6 and 8

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