Standard Deviation Example Example taken from the following website http://www.mathsisfun.com/data/standard-deviation.html

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

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

Now subtract the mean from each dog height (x - μ) 600 - 394 470 - 394 430 - 394 170 - 394 300 - 394

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

Σ(x - μ)2 Now, find the sum of all those squared numbers 42436 + 5776 + 50176 + 1296 + 8836 = 108520

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

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

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