Download Standard Deviation Example

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)
600  470  170  430  300
 394
5
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
(x - μ)2
Now, find the sum of all those squared numbers
Σ(x - μ)2
42436 + 5776 + 50176 + 1296 + 8836
= 108520
Take that sum number and
divide by how many numbers
you have.
Σ(x - μ)2
n
108520
5
= 21,704
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.