Question About Averages and Percentages Over Time

JoeB5841

New Member
Joined
Nov 18, 2013
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7
Hi all, I've lurked and found many answers on this site in the past, but now it's time to post.

This is less of an Excel question and more of a general math question. Here's the background -

At work we have employees who process our billing. They take completed work orders from the field, and process them into invoices that we send out to our customers for payment. They have a daily goal of clearing out their queue of work orders that are ready each morning to be invoiced. The goal is different each day, if that matters.

I am being asked to come up with a way to quantify how well they are actually doing toward this goal. I need to assign a percentage to each day's work, and then assign a percentage over a period of time (let's say a workweek). If the goal one day was to complete 222 invoices, and they completed 205, then they did 92.3% of their work that day. I run into a conundrum when I want to take an average of the workweek. I've attached a sample image of what I'm working with.

The question I am asking is - Do I want to take an average of all of the daily percentages? (Method A in the picture) Or.. should I take the percentage of an average of the daily numbers? (Method B in the picture)

In the attached image, you'll see that the two methods produce different results. Which method is mathematically "preferable?" This is probably something I learned as a teenager!

AorB.jpg
 

Excel Facts

Why does 9 mean SUM in SUBTOTAL?
It is because Sum is the 9th alphabetically in Average, Count, CountA, Max, Min, Product, StDev.S, StDev.P, Sum, VAR.S, VAR.P.
Assuredly Method B. Otherwise Goal=1 and Today=0 is weighted equally with Goal=100 Today=50.

Also, I'd total the Goal and Today numbers rather than average. The result will be the same, but it's more obvious what you're doing.
 
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Assuredly Method B. Otherwise Goal=1 and Today=0 is weighted equally with Goal=100 Today=50.

Also, I'd total the Goal and Today numbers rather than average. The result will be the same, but it's more obvious what you're doing.

Thanks, and you bring up a good point about weight that I was missing. So just to clarify, you're saying that Method A does not account for the fact that each day's workload is not the same. In other words, each of the daily percentages represents values that have different weights day-to-day.

In contrast, by totaling the values from each day in both "Goal" and "Invoiced" columns and then finding the percentage of that total, Method B properly weights the daily values and the resulting percentage is a more accurate depiction of the work being done?
 
Upvote 0
Yup. Except

Goal=1 and Today=0 is weighted equally with Goal=100 Today=50.

should be

Goal=1 and Today=0 is weighted equally with Goal=100 Today=0.
 
Upvote 0

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