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The Flaw of Averages
By JLP | October 9, 2006
My last post reminded me of how misleading the standard average can be. Granted this example is a bit extreme, but assume there is a town with 50 families. All but one of the families has a net worth of $50,000, while one family has a net worth of $1,000,000. So, although only one family has a net worth over $50,000, the average net worth for the entire town is $69,000. That’s a huge difference. That’s why the median is often a more accurate picture of what is going on with the numbers. For this example, the median is $50,000.
Like I said, this is an extreme example but the it is interesting to look at. That’s why it is important to know where the numbers are coming from.
Topics: Miscellaneous | 4 Comments »
October 10th, 2006 at 8:50 am
Great post! It is amazing how numbers in the form of statistics can be used to prove anything if know one asks where the numbers can from.
October 10th, 2006 at 9:36 am
It’s not so much that “statistics can be used to prove anything” but rather that most people know so little about statistics that they don’t have the tools available to analize the validity of statements based on statistical data. We could also talk about the mode here (also 50K) or exclude outliers (1000K) and reanalyze the data. Ignornace of statistics (and math in general) is what keeps people buying $100 worth of lottery tickets or falling for schemes that tell them to “pick two consecutive numbers because they are more likely to occur.” (Why has mathmatical literacy never become as important as language literacy? Sigh.)
October 10th, 2006 at 3:34 pm
Well, in this case the median is about as useless as the average. Or, look at this case. Let’s say our fictional town has 3 people with the following net worths:
1: $0
2: $50,000
3: $157,000
The median is still $50K and the average is still $69K, but those numbers don’t give you much of an idea of the true situation of the majority of the town’s residents. From those numbers you would think the financial situation of this town’s residents is similar to the town in the original post.
But all this shows is that it’s easy to come up with contrived examples. Statistics are easy manipulated by messing with the data set, and they aren’t generally useful with a small data set.
October 11th, 2006 at 7:12 am
The flaw of averages has important implications for financial planning. Basically, any plan which assumes or relies on “average” returns has a significant probability of failure.