A Percentage of Averages

Question

A company brags about the speed of their service, "75% of our assignments are completed in an average of 20 days."

Is this a meaningful claim? Or is it kind of like saying, "60% of the time, it works every time?"

How might this be calculated?

Thanks

Answer 1

The assertion makes full sense, though there is some ambiguity in the meaning of "average.". Let $T$ be the waiting time, and let $a$ be the $75$-th percentile of $T$. Let $T^\ast=T|T\le a$.

It is not clear what is meant by average in this case, perhaps mean, perhaps median. So we are told that the mean (or median) of $T^\ast$ is $20$.

Answer 2

I just wanted to add an example of the calculation, assuming that average refears to the arithmetic mean, which does not have to be the case as stated in André Nicolas' answer.

Assume you are talking about 8 assignments overall and the processing time of each assignments in day is given by (randomly):

1 3 5 10 3 8 100 4 

Now, if you are the company, you advertise your fastest $75\%$, so sorting the list we get

1 3 3 4 5 8 10 100

Now taking the first $75\%$ we are left with

1 3 3 4 5 8

where the arithmetic mean is \begin{align} \frac16(1+3+3+4+5+5)= \frac{24}{6} \end{align} So the company could advertise, that $75\%$ of their assignments are completed within an average $4$ days.