Math CentralQuandaries & Queries


Question from Lisa, a student:

I would like to add up twelve percentages then divide it by 12 to get the aggregate percentage for the year. How do I accomplish this task? Thanks.

Hi Lisa,

Adding percentages os almost always a meaningless exercise. Here is an example.

You own a small corner store that has a few clothing items for sale.

In January you sold 20 items of clothing and 2 of these were hats. Thus in January 2/20 × 100 = 10% of your clothing sales were hats.

In February you sold 50 items of clothing and 3 of these were hats. Thus in February 3/50 × 100 = 6% of your clothing sales were hats.

Hence over the two months you sold 70 clothing items and 5 of them were hats. hence in the two month period 5/70 × 100 = 7.14% of your clothing sales were hats.

If you add the percentages for January and February and divide by 2 you get (10% + 6%)/2 = 8%. Hence something is 8% of what? I don't see how to give any useful meaning to the quantity 8%. If you want an annual percentage of clothing sales that arre hats you will need the raw data, the number of clothing sales for the year and the number of these sales that were hats.

I hope this helps,

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