You’re a mean one, Mr. Grinch…

I’m assuming y’all know about means. In my home school district mean, median, and mode were all taught in third or fourth grade and referenced occasionally in math classes subsequently. But I’m guessing you don’t know about types of means.

See, the mean we’re familiar with is more properly called the “arithmetic mean,” so called because it uses simple arithmetic. But there are others that show up in statistics and other scientific applications. The most common are the geometric mean, the harmonic mean, and the quadratic mean (also often called the root mean square). And all of these are based on the generalized f-mean.

Polls are useless

There are a few caveats you need to know about margins of error. A lot of people will say (and I have in the past been guilty of this lapse) that a confidence interval or margin of error represents the range in which there is a 95% chance that the population mean falls. This is not true. For example, let’s imagine that we’ve taken seven polls in a week, and we don’t expect that anything has significantly changed between them (Romney has not shot a dog; Obama has not worn a turban), and we get these results:

 Romney Obama Margin of Error 45% 55% ±2% 48% 52% ±3% 50% 50% ±2% 48% 52% ±4% 46% 54% ±2% 47% 53% ±1% 59% 41% ±3%

So what the hell is a “margin of error,” anyway?

The year is divisible by four, isn’t it. I can tell by the noises coming out of my TV. They’re more bullshitty than normal.

It’s election season and that means that the news networks, newspapers, magazines, and blogs are awash with stories like this:

Mitt Romney leads President Obama by 3 percentage points in the deeply red state of Arizona, according to survey conducted by Public Policy Polling on behalf of Democratic think tank Project New America.

Romney leads 49 to 46 in Arizona, which is within the poll’s 3.5 percentage point margin of error. Arizona has only gone for the Democratic presidential candidate once since 1952.

So what does that mean?