Expert: Scott A Wilson - 3/16/2011

Question
Hello,

You recently posted a question to Richard J. Raridon in category Algebra:

I have a question about weighted averages.  The following is a report I get every month:
Skill    Calls offered   ACD Calls   Abandoned      %Abandoned  
Domestic     5572           5254        246            4.41
Canada       599             246        23             3.84
Exec         104              94         6             5.77
Total        6275           5918        275            4.38

I am trying to figure out how to figure the weighted average of the % Abandoned for Domestic and Exec.  Thanks for any help you can provide.

Answer
I would take the total calls for Domestic and Exec, which are 5572 and 104,
and add them together, giving 5676.  The would make the domestic calls that
were abandone 246/5676 = 0.0433 = 4.33% and the number of Exec call that were
abandoned woult be 6/5676 = 6/5676 = 0.00106 = 0.106%.

Another way to do it would be to look at the number Abandoned, which is 246 and 6,
for a total of 252.  Using this, it can be seen that Domestic calls amount to 246/252 = 97.6%
ad Excc calls result in 6/252 = 2.4%.  If you 246/6, the answer is 41.  This means that the Domestic Calls are Abandoned 41 times more often as the Exec calls.  The occurence of calls, however, makes the Domestic calls 51.1 times more often.

Statistically, an F-test could be used.  The variance is a(n-a)/n.
Compute the variance for each set and then the two sets lumped together.
The F-test would be the quotient of division between these two variances.