A simple explanation of why you can't average percents
I run into this issue frequently at work. I need a good answer that will make sense to non-math people on why they cannot average percents in the manner below. I think in pictures and am not very good at explaining in plain English!
Week 1: Total Sales = $3000, Shift One Sales = $950, Percent of Total Sales are 31.67%
Week 2: Total Sales = $2500, Shift One Sales = $800, Percent of Total Sales are 32.00%
Week 3: Total Sales = $3200, Shift One Sales = $960, Percent of Total Sales are 30.00%
To calculate the percent of Shift One Sales to Total Sales for the three week period, they should be taking the sum of Shift One Sales divided by the sum of Total Sales. Instead, they keep adding up the three percents and dividing it by 3. I can show them how this gives them different numbers (31.15% vs. 31.22%), but cannot explain in plain English why they should use method one if they want an accurate number. Does any one have a good explanation?