Posted: 11/3/2005 6:48:54 AM EDT
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Trying to set up some metrics for a process I run, and I've run into a snag. I'm calculating on-time rates for staff packages. It should be pretty simple: # on time or early = on time rate. total # of packages Here's the rub--the packages are being done by a variety of offices. When I average the on-time rate (expressed as a percentage) for the 24 different offices, I get a DIFFERENT on-time rate (85.1%) than for my overall rate calculated from the total # of packages (74.5%). My question--shouldn't they be the same? I know there would be a little difference due to rounding errors, but a 13% difference seems significant to me. |
You need to do a weighted average. Take an individual office's on-time rate multiplied by its number of packages and sum those for all offices. Then divide by the total number of packages and you'll get the average. For example, suppose Jim does 20 assignments and Joe does 10. Jim performs all twenty on time (100% rate) but Joe only does 5 (50%). If I just averaged the two percentages 100% and 50%, I would get 75% when the actual average percentage is ((20*100%)+(10*50%))/30, or 83.33% |
they don't have to be the same. It's because when you average the rates, you apply an equal weight to each rate, even though one rate may be arrived at from a WAY larger number of packages. So 1/2 = 50% counts as much towards your average as 5000/20000 = 25% giving you (50% + 25%)/2 = 37.5% but if you add up the packages you get 5001/20000 = 25.005% If the total number of packages for each office was the same, ith only the ontime rates differing, then the average of the rates would work. |
for an overall rate, add up all on time packages for all offices and divide by the total number of packages for all offices. That would be the same as a weighted average of the indivudal offce rates (assuming your weighting by the number of packages per office). |
Excellent, that's exactly what I needed. Thanks for your help! |