Q9 of 44 Page 80

The arithmetic mean of a group of 75 observations was calculated as 27. It was later found that one observation was wrongly read as 43 instead of the correct value 53. Obtain the correct arithmetic mean of the data.

Given that, the total number of observations = 75

Mean of 75 observations = 27


Mean is given by,



⇒ Sum of all observation = Mean × Total number of observations


⇒ Sum of all observation = 27 × 75 = 2025


Now, according to the question, one of the value in the observation was wrongly taken as 43 instead of 53.


So, in order to obtain the new mean, we need to subtract 43 from the sum of observations and add the correct value, 53 to it.



⇒


⇒


Thus, the new mean = 27.13


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