average and total average

Question

why is it when I get the average of the column "per hour", it's different from the total?

Answer 1

Let's normalize some of the numbers. For cases, I'll divide by $1140$. For hours, I'll divide by $103.01$.

ASC              CASES    HOURS
Feeder/Invoices   3.26     1.82
Manual            2.59     2.94
Audit/Processes   2.26     7.63
Other             1.00     1.00

As you can see, the number of hours for Audit/Processes is much larger than the other ASCs, while the number of cases doesn't vary as much. This results in its lower per hour rate of $3$ having a larger sway than the other ASCs, since it alone represents over half the total hours.

If the number of hours or the number of cases were equal for each ASC, then you could just take the average of the per hour rate and it would work. But since the weight of each ASC is not equal in regard to a per hour total, you can't just take the average of them.

Answer 2

Your total column is weighting the per hour numbers by the number of hours.

That is, if you straight average the per hour numbers, $$ (20+10+11+3)/4 = 11, $$ you are not getting the average number of 'per hours' because there is more time spent on 'audits' than on 'invoices'

The actual average would be $$ 10379/1379.70 = \frac{(785.84*3 + 302.65*10 + 188.20*20 + 103.01*11)}{(785.84+302.65+188.20+103.01)} = 7.5 $$