[quote=AN]CONCHO, I agree that median and average have their flaws. However, if you think it’s nearly worthless, then do you have a suggestion of something better that allow us to do our own data mining including historical data? I take median and average data over anecdotal any day of the week. Or, are you saying since median, average, and anecdotal are all nearly worthless, so there’s no point in discussing about it?[/quote]
Yeah, you can’t make any assumptions based on mean. For example, here are two populations:
Population A: 100,000 people earning between 25,000 and 75,000 a year, with a perfect normal distribution. Mean income 50,000.
Population B: 100,000 people, 99,000 of whom earn 10,000 a year and 1,000 who earn 10,000,000 a year.
Population A has a single-mode income distribution, population B has a dual-mode income distribution. Population B has a much higher standard deviation of income than population A.
Gross income of Population A: 5,000,000,000
Gross income of Population B: 10,990,000,000
Average income of Population A: 50,000/year
Average income of Population B: 109,900/year
Looking at only average and gross income, it appears that population B is much more prosperous than population A. Which would you rather live in? Based on average income, you’d choose population B of course. However if you knew that population B had an extreme bimodal income distribution, you’d pick population A. Perhaps this is why our media and government love to tell us averages but never provide standard deviation.
Standard deviation is so handy because it is a single number that gives us an instant insight into the type of distribution we’re looking at. It doesn’t require the reader to parse a huge table of figures or mounds of data; instead it is a clever distillation that is almost as easy to calculate as the average. There’s really no reason not to include it in a statistical study other than ignorance or deliberate obfuscation in order to mislead the reader.
In the absence of data about the underlying distribution, it is preferable not to make any assumptions about the data since you are likely to be wrong.
