The average of the squared differences from the Mean.

To calculate the Variance, take each difference, square it, and then average the result:

variance calc

So the Variance is 21,704

And the Standard Deviation is just the square root of Variance, so:

Standard Deviation
σ = √21,704
= 147.32…
147 (to the nearest mm)

So, using the Standard Deviation we have a “standard” way of knowing what is normal, and what is extra large or extra small.

Rottweilers are tall dogs. And Dachshunds are a bit short … but don’t tell them!

But … there is a small change with Sample Data

Our example has been for a Population (the 5 dogs are the only dogs we are interested in).

But if the data is a Sample (a selection taken from a bigger Population), then the calculation changes!