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

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MARKS Content Team · Accepted Answer

Correct answer: (D) 5 and 6. x¯=4,N=5 and (Σx-x¯^2)/N=2.8 ⇒Σx-x¯^2=2.85 ∴Σx-x¯^2=14 ∴2-4^2+2-4^2+5-4^2+α-4^2+β-4^2=14 Where α,β are the other two observations. ∴4+4+1+α-4^2+β-4^2=14 ∴α-4^2+β-4^2=5 Also, (2+2+5+α+β)/5=4 ∴α+β=20-9=11 Clearly 5,6 only satisfy the above equations in α,β. Hence, the required numbers are 5,6.

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

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