The Compulsive Coder

Averages and Standard Deviation

I frequently deal with marketers and marketing departments and am just as frequently astounded by how ignorant most marketers are of how to apply mathematical and statistical practices to their trade.One fundamental stands out most prominently: the meaning and power of calculating standard deviation when examining averages.

Marketers love to talk about averages. However, the most important part of an average is almost always overlooked: standard deviation.

The best way for marketers to look at standard deviation is to view it as a measurement of consistency.

Let’s say you’re the coach of a football team and it’s fourth down with four yards to go to the end zone. You have two running backs, one who averages five yards with a standard deviation of two yards and another who averages seven yards with a standard deviation of five yards. (Kudos to MathGeek for this example).

Which back do you choose? The correct answer is the first back, because he’s more consistent. While he’s not likely to bust a run for big yards, he’s also not as likely to get stuffed at or behind the line of scrimmage.

A more applicable example is average order size. Companies LOVE to talk about average order size. One of our clients’ average order size is about $160. But the standard deviation is $256!

What’s this mean to a marketer? It means that in this case average order size is totally and completely meaningless as order sizes are all over the place. It means that if you look at 1000 orders very few of them will be close to $160. Any effort focused on increasing average order size would be a waste of resources because the focus would be upon a segment that doesn’t exist…there simply aren’t very many customers making orders at $160.

A better practice would be to examine a frequency distribution of order sizes to determine the ranges in which most orders are placed…but that’s an issue for another posting.

So how does one calculate standard deviation?

Simple! It’s the square root of the sum of the squares of the differences from the statistical mean divided by the degrees of freedom.

Ok, so it’s not so simple, but spreadsheet software packages like Microsoft Excel or OpenOffice Calc make it simple for you.

You know how you can highlight a range of numbers, say A1 to A10 and somewhere else on a the spreadsheet, maybe A11, type “=SUM(A1:A10)” and you get the sum of those number? Just do the same thing, except instead of SUM put “STDEV”…so you’d have “=STDEV(A1:A10)”.

It’s that easy. Excel or Calc does all the heavy lifting.