Identifying outliers with standard deviation

Here's a histogram of the actual data we were looking at in the preceding example for calculating variance.

Now we see that the number 4 occurred twice in our dataset, and then we had one 1, one 5, and one 8.

The standard deviation is usually used as a way to think about how to identify outliers in your dataset. If I say if I'm within one standard deviation of the mean of 4.4, that's considered to be kind of a typical value in a normal distribution. However, you can see in the preceding diagram, that the numbers 1 and 8 actually lie outside of that range. So if I take 4.4 plus or minus 2.24, we end up around 7 and 2, and 1 and 8 both fall outside of that range of a standard deviation. So we can say mathematically, that 1 and 8 are outliers. We don't have to guess and eyeball it. Now there is still a judgment call as to what you consider an outlier in terms of how many standard deviations a data point is from the mean.

So that's something you'll see standard deviation used for in the real world.