I’ve noticed a lot of people in the HBD-o-sphere, including some very prominent bloggers, don’t know diddlysquat about statistics, so I am going to do a brief series on some basic concepts.

The first is my absolute favorite: The standard deviation represented by the Greek letter sigma, σ.

I remember learning about this in high school. I don’t know how I learned it, because God knows none of my teachers knew what a standard deviation is, but once I discovered it, I was so excited, because it’s one of the most fascinating concepts in the World.

Most of you know what a mean is. A mean, also known as an average, is simply the sum of a bunch of numbers, divided by the number of numbers.

174,193,185,174,170,177,191,173,179,175,170,180,178,180,168,178,188,180,180,175

170,168,160,172,158,162,155,173,157,160,170,160,160,173,160,168,162,163,163,168

In order to determine the standard deviation, you take the square root of the average squared difference from the mean of the 40 heights. This number is sometimes adjusted for what’s known as degrees of freedom, but we wont discuss that now.

The standard deviation is an enormous amount of work to calculate by hand, so you use this excellent online calculator which shows the standard deviation is about 9.5.

Why should you care?

Because when the distribution of numbers is normal, the standard deviation has some fascinating properties. Roughly two thirds of the sample (68%) will fall within one standard deviation of the mean, so in our sample, two thirds should fall from 162 cm and 181 cm. In our sample it’s a little more (about 78%).

In a normal distribution, 95% should fall within two standard deviations of the mean, so in our sample, between 153 cm and 191 cm. In our sample, it’s a bit more than expected (98%). Our sample might not be perfectly normal because we combined men and women together.

In a perfectly normal curve, only 0.1% of values fall more than 3 standard deviations above the mean, and only 0.1% fall more than 3 standard deviations below the mean.