Question

Mean of 100 observations was found to be 30. If three observations were wrongly taken as 53, 23 and 12 instead of 16, 18 and 27, find the correct mean.

• A. 29.93
• B. 27.73
• C. 29.63
• D. 29.73

Answer 1

The correct option is D 29.73

We know,
Mean = $\frac{Sumofallobservations}{Numbersofobservations}$
Given, incorrect mean = 30
and numbers of observations = 100

Incorrect mean = 30 = $\frac{Sumofincorrectobservations}{100}$
$\Rightarrow$ Sum of observations = 30 X 100
$\Rightarrow$ Sum of observations = 3000

So, sum of all correct observations
= 3000 - (53 + 23 + 12) + (16 + 18 +27)
[Since, wrong entries should be removed or subtracted and right entries should be added]

= 3000 - 88 + 61
= 2973
Correct Mean = $\frac{2973}{100}$
Correct Mean = 29.73

Thus, correct mean of the observations is 29.73.