The mean and median of 100 observations are 50 and 52 respectively. The value of the largest observation is 100. It was later found that it is 110 not 100. Find the true mean and median of the observations?

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50,52

50.1, 52

51,52

53,52

answer is B.

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Detailed Solution

we know that Arithmetic mean =

\sum_{}^{} \frac{x}{N}

Given Mean =50
N=100
i.e, 50=

\frac{\sum_{}^{} x}{100}

\Rightarrow

∑X=5000
Later found that it is 110
So the 100 items is wrong value correct A.M =

\frac{[\sum X (wrong) + correct value of observation - Incorrect value of observation]}{N}

correct Mean =

\frac{[5000 + 110 - 100]}{100}

\frac{5110 - 100}{100}

\frac{5010}{100}

=50.10
∴ The real or true mean value is 50.10
Median value is 52

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