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Why is my math wrong?
I am trying to figure out why my percentages are wrong here. I am calculating the percentage of change in sales from one month to another.
In the first month, we have $43,731.05 (raw sales) minus $4,061.91 (returns) to get a total of $39,669.14 (sales after returns).
In the second month, we have $34,377.57 (raw sales) minus $3,724.19 (returns) to get a total of $30,653.38 (sales after returns).
Here comes the tricky part. I calculate that the change in raw sales from month one to month two is -21%. This is because there were less sales.
I calculate that the change in returns from month one to month two was -8%. This is because there were less returns.
And I calculate that the change in sales after returns from month one to month two was -23%.
Now, if raw sales were down 21% but returns were down 8%, then why would my total be down 23%? Shouldn't it be lower than 21%? Wouldn't the drop in returns mean that the percentage total in sales after returns be lower than the raw sales percentage?
Please explain what I'm doing wrong here.
What you are doing wrong is comparing two different things. If you were starting from the same base, you would have reason to worry about your calculations, but a raw percentage drop in returns does not necessarily combine with a raw percentage drop in raw sales to result in a raw percentage drop in final sales - the reason is that the original raw returns are different as measured by percentage of raw sales.
In the first example, returns are 9.3% of raw sales. In the second, returns are 10.8% of raw sales - as you can see, returns as a percentage of raw sales are actually up - which is why final sales were down more than raw sales.