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The mean of 10 observations was calculated as 40. It was detected on rechecking that the value of 45 was wrongly copied as 15. Find the correct mean.

User KeyNone
by
7.7k points

1 Answer

4 votes

Explanation:

the mean value is the sum of all data points divided by the number of data points.

so, in our case

40 = (a + b + c + d + e + f + g + h + i + j)/10

and therefore

00400 = (a + b + c + d + e + f + g + h + i + j)

we don't know the individual data points. but we don't have to when solving this problem.

all we need to know is that one of these data points should have been 45 but was used as 15 in the calculation.

so, when we correct that data point, we suddenly add 45 - 15 = 30 to that data point and therefore to the whole sum.

400+30 = (a + b + c + d + e + f + g + h + i + j) + 30

430 = (a + b + c + d + e + f + g + h + i + j + 30)

the new (correct) mean value is now the new sum (430) divided by 10 (the number of data points) :

430 / 10 = 43

User Howard Rothenburg
by
8.5k points
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