1. Standard Deviation Example
Example taken from the following website

2. A vet measures the height of 5 dogs....
The heights (at the shoulders) are: 600mm, 470mm, 170mm, 430mm and 300mm.

3. Find the standard deviation of the dog heights
First find the mean (μ)

4. Now subtract the mean from each dog height (x - μ)

5. Next, take each of the differences just found and square them
(206)2 = 42436
(76)2 = 5776
(-224)2 = 50176
(36)2 = 1296
(-94)2 = 8836

6. Σ(x - μ)2 Now, find the sum of all those squared numbers =

7. This number is called the variance.
Take that sum number and divide by how many numbers you have.
Σ(x - μ)2 n
108520
= 21,704 5
This number is called the variance. σ2

8. √ √ Finally, take the square root of the variance Σ(x - μ)2 n 21,704
147.3
This number is the standard deviation σ

9. The standard deviation shows which dogs fall under “normal” height and which dogs are too tall or too short.