Math CentralQuandaries & Queries


Question from Camilla, a student:

I was recently asked: if a store sells a certain syle of skirt, an in the first week they sell 13, in the second week 20, in the third week 17 and in the fourth week 23, calculate the percentage difference between the highest and the lowest weekly sale. I'm not sure how to work it out! Thanks!

We have two responses

Hi Camilla. I'm not surprised it is a bit confusing.

When we talk about percentages, they don't make sense unless it is clear what we are taking a percentage of.

Most of the time, when we are asked about percentage differences, they really mean "what percentage of the earlier value should be added (or subtracted) to the earlier value to get the later value." For example, if a store sold a skirt for $20 and increased the price to $30, then the percentage difference (in this case, the percentage increase, because it went up) is 50% because $20 + $20×50% = $30.

In your question, we clearly have two values, 13 and 23 as the highest and lowest weekly sales. But what is the percentage difference between them? This is a really ambiguous use of the term and it is just due to chance that the two values are the earliest and latest values in the list.

I would say that there is no properly correct answer, because the term percentage difference is too vague in this context. However, the least incorrect answer is probably the percentage by which you multiply 13, then add it to 13, to get 23. In other words, $13 + $13×P = $23.

Sorry to be of so little help, but some questions are worded better than others.
Stephen La Rocque.



I agree completely with Steve's comments. There is a great deal sloppiness in the language we use when talking about percentages. Whenever you see or hear the word percentage you should ask "Percentage of what?" In your question I would feel more confident about Steve's "least incorrect answer" if you had asked for percentage change rather than percentage difference. Percentage change indicates that the quantity is changing over time and you want the change as a percentage of the earlier value as is Steve's interpretation. Percentage difference does not indicate any order and I have no idea if you want the difference as a percentage of the smaller value or as a percentage of the larger value.


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