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The mean of a data set consisting of 20 observation is 40. If one observation 53 was wrongly recorded as 33, then the correct mean will be

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42.5

answer is A.

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Detailed Solution

Mean of 20 observations 40

one observation 53 wrongly recorded as 33.

$\begin{array}{rcl} x & = & \frac{\sum x_{i}}{20} = 40 \Rightarrow \sum x_{i} = 800 \\ \sum X & = & 800 - 53 + 33 = 820 \end{array}$

Correct Mean $= \frac{\sum X}{20} = \frac{820}{20} = 41$

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