Hi,

SUMMARY: I'm currently using a weighted average for my services but want to
used a statistically sound and defensible alternative to a weighted
average such that I end up with the highest rate possible. I was
thinking that perhaps some option pricing method might get me to that
higher number.

Question: What is a statistically sound and defensible way for me to calculate
my "average" such that I get the highest number possible? Please
explain and provide a formula I can use.

DATA:
Here's a sample of my data:

	          Rate 	          Amount         Units 
company 1	 $37.84 	 $54,527.00 	 1,440.99 
company 2	 $73.97 	 $60,000.00 	 811.14 
company 3	 $50.41 	 $127,789.00 	 2,534.99 
company 4	 $89.77 	 $20,247.00 	 225.54 
company 5	 $74.65 	 $63,611.00 	 852.12 
company 6	 $91.09 	 $34,843.00 	 382.51 
company 7	 $74.85 	 $46,286.00 	 618.38 
company 8	 $69.56 	 $301,044.00 	 4,327.83 
company 9	 $44.12 	 $102,226.00 	 2,317.00 
company 10	 $88.32 	 $176,818.00 	 2,002.02 
company 11	 $63.26 	 $61,396.00 	 970.53 
company 12	 $49.41 	 $2,000.00 	 40.48 
company 13	 $72.75 	 $7,292.00 	 100.23 
company 14	 $91.09 	 $137,611.00 	 1,510.71 
company 15	 $75.02 	 $95,294.00 	 1,270.25 
			
Total	 $1,046.11 	 $1,290,984.00 	 19,404.74 
Weighted Average	 $66.53 		

I currently calculate a weighted average. I want to get to a higher
number and be able to support it.

Thanks,
Patrick

Patrick, you're in luck as you have several (simple) alternatives!

I took your data and plugged it into Excel to figure out the following:

A) Geometric mean: $67.44
   Way to figure it out: take the n-th root of (X1)times(X2)times(X3)...(Xn) 
   where the X's are your rates for different companies, and n in this case,
   would be 15, since you have 15 companies.

A) Arithmetic mean (classical definition of "average"): $69.74
   Way to figure it out: $1046.11 divided by 15 (number of companies)

B) Median: $73.97
   Way to figure it out: The median is the middle value in a set of numbers.
   Sort the data in ascending order, and then pick out the middle value.
   This method may yield better or worse values depending on the circumstances.

C) Mode: $91.09
   Way to figure it out: The mode is the most common or "most frequent" value   
   in a set.  This may be very biased under certain circumstances.

Hope this bit helps.