4.4 Mean, variation, standard deviation and coefficient of variation

Owned by Tessa Jacobs
Last updated: nov. 17, 2023
2 min read

In statistical terms continuous variables are described by a mean and measures of variation. To describe the variation, standard deviation, variance and coefficient of variation can be used.

The mean is calculated as follows:

The "mean" of a sample is the sum the sampled values divided by the number of items in the sample:

For example, the arithmetic mean of five values: 4, 36, 45, 50, 75 is

 

The variance is calculated as follows:

S2=∑(Xi-X)2 /(N-1)

The standard deviation is calculated as follows:

For example the standard deviation is the square root from the variance and in this case for the five values: 4, 36, 45, 50, 75 is to be calculated as:

N=5 and the mean for x= 42

Xi

Xi-X

(Xi-X)2

4

-38

1444

36

-6

36

45

3

9

50

8

64

75

33

1089

∑Xi= 210



∑(Xi-X)2=   2642

In this case the variance is 2642/4 =660.5 and the standard deviation is √2642/5= 32.5

The coefficient of variation is the standard deviation divided by the mean and is calculated as follows:

In this case µ is the indication for the mean and the coefficient of variation is: 32.5/42 = 0.77. This means that the size of the standard deviation is 77% of the size of the mean. This implies that you see a lot of differences among animals when the five values above are the value of a trait of five animals.