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The mean and variance of eight observations are 9 and 9.25, re

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The mean and variance of eight observations are 9 and 9.25, respectively. If six of the observations are 6, 7, 10, 12, 12 and 13, find the remaining two observations.

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The mean and variance of eight observations are 9 and 9.25, respectively. If six of the observations are 6, 7, 10, 12, 12 and 13, find the remaining two observations.

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Text solutionVerified

Solution:

6, 7, 10, 12, 12, 13, a, b

\overline{x} = \frac{\sum x _{i}}{n}

\frac{60 + a + b}{8} = 9

a + b = 12

σ^{2} = \frac{\sum ( x - x ) ^{2}}{n}

= \frac{3 ^{2} + 4 + 1 + 9 + 16 + ( a - 9 ) ^{2} + ( b - 9 ) ^{2}}{8}

= 9.25

39 + (a - 9)^{2} + (b - 9)^{2} = 74

a^{2} + b^{2} - 18 (a + b) + 162 = 35

a^{2} + b^{2} - 216 + 162 = 26

a^{2} + b^{2} = 80

eqn(1)

a + b = 12

eqn(2)
when a=8 , b=4
when a=4, b=8

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Question Text	The mean and variance of eight observations are 9 and 9.25, respectively. If six of the observations are 6, 7, 10, 12, 12 and 13, find the remaining two observations.
Answer Type	Text solution:1
Upvotes	150

The mean and variance of eight observations are 9 and 9.25, respectively. If six of the observations are 6, 7, 10, 12, 12 and 13, find the remaining two observations.

Text solutionVerified

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