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title: "4.4 Mean, variation, standard deviation and coefficient of variation"
canonical: "https://wiki.groenkennisnet.nl/space/TAB/283377723/4.4%20Mean%2C%20variation%2C%20standard%20deviation%20and%20coefficient%20of%20variation"
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---
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:

> ℹ️ ![image](media://3ff69988-0bc9-45ce-9d0e-117f657366b1)

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

> ℹ️ ![image](media://bc8ac3ec-02ac-4140-84ae-028840796e44)

*The variance is calculated as follows:*

> ℹ️ *S*<sup>*2*</sup>*=∑(X*<sub>*i*</sub>*-X)*<sup>*2*</sup>* /(N-1)*

*The standard deviation is calculated as follows:*

> ℹ️ ![image](media://c6c5a29e-5143-46b2-b1f3-f2441eb89c49)

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

|  |  |  |
| --- | --- | --- |
| **X**<sub>**i**</sub> | **X**<sub>**i**</sub>**-X** | **(X**<sub>**i**</sub>**-X)**<sup>**2**</sup> |
| 4 | -38 | 1444 |
| 36 | -6 | 36 |
| 45 | 3 | 9 |
| 50 | 8 | 64 |
| 75 | 33 | 1089 |
| ∑X<sub>i</sub>= 210 |  | ∑(X<sub>i</sub>-X)<sup>2</sup>=   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: *

> ℹ️ ![image](media://1d6c5b26-e019-48b7-a250-95032213663a)

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.