Question

Arithmetic mean of 9 observations was calculated as 45. In doing so an observation was wrongly
taken as 42 for 24. What would then be the correct mean?
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Answer 1

Mean of 9 observation =45.

xˉ=45

n=9

xˉ=n∑x

∑x=xˉn=45×9=405

Sum of all observation are 405.

Now an observation was wrongly taken as 42 for 24.

∴ 42−24=18 was mistakely added more.

∴ ∑x−18=387=∑y  [the correct sum of all observation.]

∴yˉ=n∑y=9387=43 

∴43 is the correct mean.