# How to determine stats to reach a certain average

This has me a bit boggled and I even tried using the What-If Analysis in Excel to figure it out..

Statistics are these:

• A call center takes in roughly 100 calls a day
• The average time to answer the calls so far is 60 seconds
• There are 30 days in the month
• The current day of the month is 10

Is there a way to find out how many calls at what average Time to Answer in order to bring down the average from 60 seconds to 45?

Clairification Example

• Today is August 10th and so far there have been 1,000 calls
• The average Time-to-Answer so far is 60 seconds

Answer: It will take X more calls at Y (average Time to Answer) to reach an average time-to-answer of 45 seconds.

• This will range of course due to being a double variable, it will take a higher number of calls at a higher average time to answer and likewise for lower.

The relation is $$60\cdot 1000 + Y\cdot X = 45\cdot(1000+X)$$ where $$X<=2000$$
Therefore $$Y=45-{15000\over X}\leq37.5$$ seconds per call.
Also since $$Y\geq0$$ we know $$X\geq 334$$ calls.