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  • The mean and standard deviation of a set of 99 observations are 50 and 2 respectively. If the 50 th observation is 46 , find the median of the remaining 49 observations.

The mean and standard deviation of a set of 99 observations are 50 and 2 respectively. If the 50 th observation is 46 , find the median of the remaining 49 observations.

Option: 1

36


Option: 2

45


Option: 3

48


Option: 4

51


Answers (1)

best_answer

The median of the remaining 49 observations is the same as the (49+1) / 2=25 th observation.
Let the 25th observation be \mathrm{x}
Then, we have:
\mathrm{ E(x)=46 }
\mathrm{ \operatorname{Var}(x)=2 \wedge 2=4 }
By the 50-50 rule, we have:
\mathrm{ E(x)=(50 \star 46+49 \star x) / 99 \\ }
and 

\mathrm{ \operatorname{var}(x)=(49 * 4 \wedge 2) / 99 }
Solving the above equations, we get:
x=48 
Therefore, the median of the remaining 49 observations is 48 .

Posted by

Gaurav

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