Standard Deviations

I suspect that the majority of market participants haven’t thought much about the statistical concept of standard deviations since their university days. While statistics may have seemed dry and dreary in college, a necessary evil on the way to education when applied to the markets that we all have a passion for trading they are really quite fascinating.

Standard deviation measures the spread of data distribution. The more spread out a data distribution is, the greater its standard deviation.

For example, the blue distribution on the bottom has a greater standard deviation (SD) than the green distribution on top:

Dispersion is the difference between the actual value and the average value. The larger this dispersion or variability is, the higher the standard deviation. The smaller this dispersion or variability is, the lower the standard deviation.

Interestingly, the standard deviation cannot be negative. A standard deviation close to 0 indicates that the data points tend to be close to the mean (shown by the dotted line). The further the data points are from the mean, the greater the standard deviation.

Mean means an average of the numbers.

First, we need a data set to work with. Here’s a good one: 6, 2, 3, 1

The formula for the standard deviation (SD) is

The standard deviation is the square root of 3.5 is 1.87.

The higher the deviation, the more it tends to get attracted towards the mean. In this case, it is a median Bollinger. But it’s not actually a median. It’s mean.