Question

arithmetic mean of 9 obeservations is calculated as 38 .But doing so ,an observation 27 is mistaken for 72 . find the actual mean of the data

Answer 1

Mean=sum of observations/ total observations
38=sum/9
38×9=sum
342=sum
If a number is mistakenly written as 72 then 45 should be added to the sum
sum=342
actual sum should be :
342+45
=387
mean=sum/total observations
=387/9
= 43

Answer 2

let x1.......x9

mean = x1+x2+x3+.........x9/9

38= x1+x2+x3.......+x9/9

x1+x2+ x3 ....+x9= 342

27 mistake for 72 so 72-27= 45

342+45= 387

correct mean = 387/9 = 43

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