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Question

The mean of five observations is 4 and their variance is 5.2 . If three of them are 1, 2, 6, then other two are

A
2, 9
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B
4, 7
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C
5, 6
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D
2, 10
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Solution

The correct option is C 4, 7
Number of observations =5
Mean ¯x=4 and x=1,2,6,a,b
σ2=(xi¯x)2N(N=5)
(xi¯x)25=5.2 or (xi¯x)2=26 (i)
(14)2+(24)2+(64)2+(a4)2+(b4)2=26
(a4)2+(b4)2=9 (*)
(Here a, b are unknown quantities)
By cross check we find only the number 4 and 7 satisfies the equation (*)

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