Averages

fwiz · 2007-12-20 01:59:32

HI all,

I've got a wee problem with averages, I use these values all the time for work, On a daily basis I create a file in excel that works out a percentage value for 30+ people, I need to put these values for all people into a table to get weekly and monthly average values from the percentages. I've been told that mathematically you cannot average percentage values ? is this correct ?

TheDude · 2007-12-20 02:09:45

What are these percentages of? Total pay, hours worked, units sold?

Last edited by TheDude (2007-12-20 02:10:44)

fwiz · 2007-12-20 02:17:25

Pretty difficult to explain.. i'll try, we have a resource schedule that uses decimalised hour/mins to work out headcount budget to cover what is required for daily tasks, each task performed has a timing against so we know how long they have spent working on a task based on the volumes they have processed, I then take this value and then divide by the total hours worked, 100% value means they have worked as expected lower than 100% means they are not performing, above 100% working above objectives. I need to collate this daily info into a weekly table and work out an average for that week, the same for the monthly. the monthly values will then be added to a yearly table to produce a yr to date average. Since I've been told you cannot average percentage values - I'm a little stuck

mathsyperson · 2007-12-20 02:34:46

So for each day you've got a "volume produced" value and an "expected volume produced" value, which you combine to make a percentage.

It sounds like what you're currently doing is taking values for each day, making a percentage of each, and averaging the percentages.
Instead, you should be averaging the actual and expected volumes and then taking the percentage using those averages.

Here's an example - let's say you've got two underproductive workers, Adam and Brett, and you want to decide which should be fired. Here are their results for two days:

Monday

| Expected Volume | Actual Volume | Productivity (%)
----------------------------------------------------------------------
Adam | 100 | 66 | 66
Brett | 40 | 24 | 60

Tuesday

| Expected Volume | Actual Volume | Productivity (%)
----------------------------------------------------------------------
Adam | 200 | 180 | 90
Brett | 500 | 430 | 86

Adam had a higher percentage on both Monday and Tuesday, so he was the better worker. Right?
Well, combining the two days into one table gives this result:

Both days

| Expected Volume | Actual Volume | Productivity (%)
----------------------------------------------------------------------
Adam | 300 | 246 | 82
Brett | 540 | 454 | 84

So overall, Brett was actually better. Finding the percentages an an intermediate stage and then combining them got you a deceptive result.
Whether you're working with daily, weekly, monthly or yearly statistics, you should always use the values rather than percentages for calculations. If you use percentages at all, it should only be right at the end for ease of information.

fwiz · 2007-12-20 02:51:25

ok I think I know what you mean now, although I have the percentage values for each day - I can use them on a daily basis, however if I am to use on a weekly/monthly basis then I must use the figures to obtain my percentages not the actual percentage for each day.

this right?

mathsyperson · 2007-12-20 06:56:30

Absolutely!

luca-deltodesco · 2007-12-20 07:41:02

if you want to see it mathematically. heres an example with 2 sets of data.

ratio 1 = A1/B1
ratio 2 = A2/B2

if you average them you get: (A1B2+A2B1)/(2B1B2)

but if you average the data sets, and get the ratio you get

½(A1+A2) / ½(B1+B2) = (A1+A2)/(B1+B2) which is quite obviously very different from the above

Math Is Fun Forum

#1 2007-12-20 01:59:32

Averages

#2 2007-12-20 02:09:45

Re: Averages

#3 2007-12-20 02:17:25

Re: Averages

#4 2007-12-20 02:34:46

Re: Averages

#5 2007-12-20 02:51:25

Re: Averages

#6 2007-12-20 06:56:30

Re: Averages

#7 2007-12-20 07:41:02

Re: Averages

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