Question on deviations from the mean

Question

If a class of 27 students has a mean score of 72 on a test, what is the sum of the 27 deviations of the scores from 72?

Answer 1

The sum of the deviations must be 0.

 

Think about it this way: for every point above the mean score of 72, there must be a corresponding point below 72, that's how averages work.

 

So if we add up all the deviations from 72, some will be positive, and some will be negative. But the total must be zero, since the mean is 72.

 

This is true for any score and for any number of students.

Answer 2

So this is really just asking if you know what an mean is.

 

The mean of 5, 6 and 10 is 7.

 

5-7 is the deviation from the mean of -2

6-7 is the deviation from the mean of -1 and

10-7 is the deviation from the mean of 3.

 

The arithmetic mean is the balance point where all the deviations cancel out.

 

So the mean of these number is 7 means that all the deviations should add to zero.

 

So if your mean is 72 ( or anything), the sum of the deviations will be 0 because that's exactly what a mean means.

 

Hope this helped.