Why is an average of an average usually incorrect? explain why taking

Karen Simpson

Karen Simpson

Answered question

2021-12-14

Why is an average of an average usually incorrect? explain why taking an average of an average usually results in a wrong answer? Is there ever a case where the average of the average can be used correctly? As an example, lets

Answer & Explanation

Archie Jones

Archie Jones

Beginner2021-12-15Added 34 answers

If there are n1,n2,andn3 students in the three schools, and the average test score for each school is a1,a2,a3, respectively, the correct average is a "weighted average:"
n1n1+n2+n3a1+n2n1+n2+n3a2+n3n1+n2+n3a3
The average of the averages is:
13a1+13a2+13a3
These two values will be exactly the same if each school has exactly the same number of students, and will tend to be "close" if the schools are relatively close in size and/or the scores for the three schools are close.
If a school system created a small school consisting of all the smartest students, they could bump up the second value - the "average of averages" - but they couldnt
Kayla Kline

Kayla Kline

Beginner2021-12-16Added 37 answers

The average of averages is only equal to the average of all values in two cases:
if the number of elements of all groups is the same; orthe trivial case when all the group averages are zero
Heres

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