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The mean of a data set consisting of $20$ observations is $40$. If one observation $53$ was wrongly recorded as $33$, then find the correct mean.
Given: The mean of a data set consisting of $20$ observations is $40$. If one observation $53$ was wrongly recorded as $33$.
To do: To find the correct mean.
Solution:
$Mean=\frac{S}{n}$
Here $S=$sum of all observations, $n=$number of observations
$\therefore 40=\frac{S}{20}$
$\Rightarrow S=800$
$\because 53$ is recorded as $33$ so we need to add $( 53−33=20)$ to get the correct mean which is
$Mean_{correct}=\frac{800+20}{20}=41$
Updated on: 10-Oct-2022
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