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Question

The mean and variance of 20 observations are found to be 10 and 4 respectively. On rechecking, it was found that an observation which was 11 was incorrectly recorded as 9. If the correct variance is V, then the value of [V] is

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Solution

¯¯¯x=xi20=10xi=200x2i20(¯¯¯x)2=4x2i=(104)(20)=2080

Now, the actual mean
xi9+1120=10.1

The actual variance
V=x2i81+12120(10.1)2V=106102.01=3.99[V]=3

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