A question about statistics and averages

[Tatsu]

My company tracks telephone performance by the number of calls abandoned, i.e. the percentage of callers that hang up before we answer their call. Our goal is <=5%.

Every month I receive a report that gives the percentage of dropped calls for the previous month, along with the raw data.

Here are the numbers for last month:

R = Received: 1437
A = Answered: 1339
a = Abandoned: 76

The number of abandoned calls is not a simple subtraction of Answered from Received but instead only unanswered calls that end after a certain time threshold. That way we are not penalized for calls that end before we have the chance to answer.

If I were calculating our performance I would do it like this:

a/R=0.05288 or 5.3%

If I were being completely merciless:

a/(R-A)=0.0681 or 6.8%

Here is how it is actually being calculated:

a/{R-[(R-A)-a]}=0.0537 or 5.4%

So my question is: What reason could they have for doing it that way?

Please have mercy, I am not a mathematician.

[Tanja]

I presume the important thing is what the remaining 22 calls were. If I understood correctly, they were calls that you did not have any chance to answer, so they may be viewed as, say, "invalid calls", so you don't want to include them in the total number of calls, so they are taken out of the equation alltogether.

[GodMark2]

Originally Posted by Tatsu

a/{R-[(R-A)-a]}=0.0537 or 5.4%

So my question is: What reason could they have for doing it that way?

Please have mercy, I am not a mathematician.

Originally Posted by Tanja

I presume the important thing is what the remaining 22 calls were. If I understood correctly, they were calls that you did not have any chance to answer, so they may be viewed as, say, "invalid calls", so you don't want to include them in the total number of calls, so they are taken out of the equation alltogether.

Or more simply, the ratio of abandoned to the total of abandoned and answered, but not counting the impossible-to-answer, which the number received would count.

a/(A+a)

Which is what that final equation simplifies to. The total received is unimportant.

[Tatsu]

Ahh... when you put it that way it makes more sense. Many thanks to you Tanja and GodMark2!

[DazzaD]

Originally Posted by Tatsu

Here is how it is actually being calculated:

a/{R-[(R-A)-a]}=0.0537 or 5.4%

As a matter of interest... is that actually how they quote the formula?

I.e. has someone said or printed that that is how they do it?

Exactly as written above?

[Tatsu]

No. It is embarrassing to admit, but that is how I worked it out for myself. I realized that I had gone the long way around the barn as soon as I read GodMark2's reply.