Comments on: Data Analysis – Do You Really Mean Average?

By: Peter Robinson

Peter Robinson — Wed, 21 Apr 2010 07:32:00 +0000

Hi Tony, thanks for raising the issues around Averages. I have long had similar discussions with computer measurement vendors. It seems that because the mean is so easily calculated using a running total and a running count of samples, it is mindlessly provided as the standard measure of computer performance when it really is quite useless for the purpose.
Jon, thanks for the book link. That looks interesting.

By: Jon Peltier

Jon Peltier — Fri, 18 Dec 2009 17:03:43 +0000

The confidence intervals are not too much better than just a central measure. Nowadays, though, you can enter a distribution, either via a distribution type and its parameters or by entering a polygon, and let Monte Carlo produce an outcome distribution.

By: Tony

Tony — Fri, 18 Dec 2009 13:53:06 +0000

Naomi – what would you provide if asked that question? I wrote to Mathias saying that using a confidence interval may be a good option. I do like the idea of plotting all of the data points. But if I could only choose one, it would probably be median.

By: Tony

Tony — Fri, 18 Dec 2009 13:50:48 +0000

I guess =arithmeticmean(x:x) may have been too long to have to write out. On another note, why do you have to type out “average” in Excel. You should be able to just type =avg(x:x).

By: Naomi B. Robbins

Naomi B. Robbins — Fri, 18 Dec 2009 12:40:36 +0000

How about giving the executives what they ask for as well as a plot of all the data?

By: Jon Peltier

Jon Peltier — Fri, 18 Dec 2009 03:05:20 +0000

In Excel, you have to use the AVERAGE function to calculate the mean. Because of this, I tend to forget that average is a more general term.

By: Jon Peltier

Jon Peltier — Fri, 18 Dec 2009 03:01:12 +0000

A client sent me a copy of the book when I helped him with some charts last month. I’d done some business modeling work with him: I built the templates and some UDFs, and he hooked the model up to a Monte Carlo routine.

Imagine my amusement when I got to the relevant part of the book, and found some of the graphs I’d made for his modeling project.

The book is easy to read, not too formal, so even some of those executives might have a chance.

By: Tony

Tony — Thu, 17 Dec 2009 22:12:54 +0000

Mathias, thanks for stopping by and leaving a comment.

Along the same lines as Naomi’s response, central tendency is measured by mean, median and mode. You are correct in that all of these functions reduce a population down to a single number. But that’s the point. How would you respond to an Executive if they were to ask directly what a typical customer size is in terms of revenue? You could answer with the arithmetic mean and median only to add a disclaimer for the faults of each OR we could introduce a confidence interval. I think going to whole distribution and standard deviations would be over most people’s heads in the corporate world.

I could say, with a 99% confidence level the typical revenue is between x and y. Most of your non statisticians probably won’t go beyond arithmetic mean (they would say “average”) or maybe median. Using a confidence interval may be the way to go. What do you think?

By: Tony

Tony — Thu, 17 Dec 2009 22:04:05 +0000

Jon, you may understand whole distribution principals, but I think in general, most executives may not even know what median is outside of the middle of two roads, which metaphorically is right on.

Thanks for the tip on the book. I’ll have to have Amazon Prime sneak it into my Christmas stocking.

By: Tony

Tony — Thu, 17 Dec 2009 21:58:29 +0000

Naomi, you are right. Mean and average don’t always translate to the same thing. There can be geometric mean, arithmetic mean, population mean, etc.. For the purposes of this post, I am referring to the arithmetic mean when I said “Mean”. I think the confusion comes from people using the term average when really meaning arithmetic mean. Again, you are correct in that mean, median and mode all measure central tendency (average).

Going back to the purpose of this post, I think the thing to take away is that if you are only providing the arithmetic mean or commonly called “average” you are really putting yourself out there in terms of accuracy risk.