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Error and Uncertainty

The mean of ...

Question

The mean of $20$ observations is $12.5$ by error one observation was noted $- 15$ instead then the correct mean is

A

11.75

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B

11

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C

14

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D

13.25

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Solution

The correct option is B $14$
Mean of 20 observation $= 12.5$
Sum of 20 observations $= 12.5 \times 20$
$= 250$
Wrong observation is -15
Correct observation is 15
So, Sum of 20 observation correctly $= 250 + 15 + 15 = 280$
First 15 is to eliminate the wrong observation and the other 15 for adding the correct observation in the data.
Correct mean $= \frac{280}{20}$
$= 14$

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