Average of percentage of 2 numbers.

Question

If I have 24081 items sold at 45% off. and 11386 items sold at 60% off.

What is the average percent off for all items sold?

Thanks for your help in advance!

Craig

(This is not homework :) )

It doesn't really matter on the prices. I actually don't need the price factor. I just need to know the average percentage discount offered rather than the discounted price. — CRAIG, Dec 04 '13 at 08:19

score 5 · Accepted Answer · answered Dec 04 '13 at 08:02

5

This is the average of $45 \%$ and $60 \%$, weighted by the respective number of items.

The total number of items is $$24081 + 11386 = 35467$$

The average percent is $$\frac{24081 \cdot 45\% + 11386 \cdot 60\%}{35467} \approx 49.82\%$$

answered Dec 04 '13 at 08:02

Zubin Mukerjee

That looks right to me. Thanks very much for the answer and for showing how to achieved it as well! – CRAIG Dec 04 '13 at 08:20

score 2 · Answer 2 · answered Dec 04 '13 at 08:03

2

It depends on the price of the items. The total percentage can be any number between 45% and 60%.

If the items all have the same price then you can just make the weighted mean of the two percentages.

answered Dec 04 '13 at 08:03

Emanuele Paolini

If you think of "percent off" as a property of each item, then I think the question is asking for the average value of that property over all items. This doesn't seem to depend on price. – Zubin Mukerjee Dec 04 '13 at 08:07
1

You are formally right, but I think that the question should be interpreted differently. It is of no interest to know the average of the percentages... what one could be interested in should be the total discount. – Emanuele Paolini Dec 04 '13 at 08:12
Makes sense, good point! +1 – Zubin Mukerjee Dec 04 '13 at 08:16
For completeness, it should still be the weighted mean of the percentages if the prices differ. Just weighted by the sum of prices in each group. – Dennis Jaheruddin Aug 26 '14 at 13:52

2 Answers2