why is it when I get the average of the column "per hour", it's different from the total?
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$\begingroup$ Can you detail your question a bit more? $\endgroup$– William HilbertCommented Jun 10, 2014 at 16:37
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$\begingroup$ Could you detail what the columns mean, how they are computed, explain your question precisely and defining the total and average you talk about... I know probability and statistics can show counter-intuitive behavior, but I am not sure what you are referring to. $\endgroup$– JoeyBFCommented Jun 10, 2014 at 16:44
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$\begingroup$ Thanks for the response, but I think @cnick sees what I'm trying to describe, sorry for not being clear. $\endgroup$– WilCommented Jun 10, 2014 at 17:08
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$\begingroup$ The column labeled "Total" doesn't even have numbers in it, so it's got to be different from one that does. So your question is not altogether clear. Are you asking why the column labeled "cases" is different from the one labeled "per hour"? $\endgroup$– Michael HardyCommented Jun 10, 2014 at 17:21
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2 Answers
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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.
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$\begingroup$ Thanks for the response, but I think @cnick sees what I'm trying to describe, sorry for not being clear. $\endgroup$– WilCommented Jun 10, 2014 at 17:08
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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 $$ 10379/1379.70 = \frac{(785.84*3 + 302.65*10 + 188.20*20 + 103.01*11)}{(785.84+302.65+188.20+103.01)} = 7.5 $$
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$\begingroup$ thank you cnick,so, just to bring it down to my level. Is it safe to say that taking an average of an average is always going to be skewed? $\endgroup$– WilCommented Jun 10, 2014 at 17:03
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$\begingroup$ Not always, but that would be a good rule of thumb. There are special cases, but when in doubt you should always go back to the original data. $\endgroup$– cnickCommented Jun 10, 2014 at 17:05
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$\begingroup$ I hope you don't mind, but, going back to my example if someone were to average out the per hour column, it would not be the same as the total on top. How would I explain that or better yet how should I represent it? $\endgroup$– WilCommented Jun 10, 2014 at 17:12
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$\begingroup$ The average calculation is above. To do the average correctly, you need to weight each entry in the per hour column accordingly. Just adding the numbers in the per hour column and dividing by 4 gives you a quantity totally unrelated to the information you have. $\endgroup$– cnickCommented Jun 10, 2014 at 17:24