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November 10, 2005
Better than Average
I love numbers. When someone or a company has a rich set of data that’s meaningful, I like to really dive in. And so I am sometimes disappointed when the only figures that are presented are “averages.” Usually that translates into people presenting or writing about an arithmetic mean. But I often crave more, as an average figure tells you nothing about the distribution of the dataset.
Wikipedia explains further,
“[Mean] is used for many purposes and may be abused by using it to describe skewed distributions, with highly misleading results. A classic example is average income. The arithmetic mean may be used to imply that most people's incomes are higher than is in fact the case. When presented with an "average" one may be led to believe that most people's incomes are near this number. This "average" (arithmetic mean) income is higher than most people's incomes, because high income outliers skew the result higher (in contrast, the median income "resists" such skew). However, this "average" says nothing about the number of people near the median income (nor does it say anything about the modal income that most people are near). Nevertheless, because one might carelessly relate "average" and "most people" one might incorrectly assume that most people's incomes would be higher (nearer this inflated "average") than they are.”
Examples like the one cited above are just the beginning. I often see statistics quoted in the popular media using “averages” which are incomplete at best, and misleading at worst. To me, averages are like snapshots as compared to a whole movie; they reveal a moment in time, but they don’t tell the whole story.
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Comments (3)
I also hate the proliferation of "junk statistics" to give the appearance of analysis. Tools like Excel make it easy to compute stats like the variance for the normal distribution so ergo everthing must be normally distributed because it's easy to calculate!
Posted by Barnaby James | November 10, 2005 11:41 PM
Posted on November 10, 2005 23:41
Ebay's announcement:
http://news.yahoo.com/s/nm/20051111/wr_nm/ebay_prices_dc
There'd be a lot of interesting data there.
Posted by Daniel Nerezov | November 11, 2005 1:13 AM
Posted on November 11, 2005 01:13
I also agree. For my business, we face seasonality on two fronts: bookings, and delivery. Using just the means would yield useless information particularly when analyzing the timing of cash flows. To account for this we have carefully modeled the seasonality of bookings and delivery. The peak season for bookings is Dec-Feb while the peak season for delivery is Jun-Aug. An order placed in May is clearly more likely to be one month away than an order placed in January. Using an average of four months for all bookings would yield a dangerously inaccurate picture of seasonal demand spikes.
Posted by Ryan Hudson | November 11, 2005 11:13 AM
Posted on November 11, 2005 11:13