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Question

# The means of five observations is 4 and their variance is 5.2. If three of these observations are 1, 2, and 6, then the other two are:

A

2 and 9

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B

3 and 8

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C

4 and 7

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D

5 and 6

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Solution

## The correct option is C 4 and 7 Let the other two numbers be α and β. ¯x=4,N=5 and ∑(x−¯x)2N=5.2⇒ ∑(x−¯x)2=(5.2)5∴ ∑(x−¯x)2=26∴ (1−4)2+(2−4)2+(6−4)2+(α−4)2+(β−4)2=26∴ (α−4)2+(β−4)2=9Also,1+2+6+α+β5=4∴ α+β=20−9=11Clearly 4,7 only satisfy the above equation in α,β.Hence required numbers are 4,7.

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