### Coefficient of variation

#### Worked example

Let us use these weights of zebu cattle as an example.

**Cow Number** | **Weight (kg)** |

1 | 280 |

2 | 295 |

3 | 245 |

4 | 310 |

5 | 285 |

**Σ x** |
**1415** |

Mean Weight () = 283 kg Standard deviation (s) = 24.14 kg

So :

CV = 24.14 / 283 = 0.0853

CV (%) = 100 × 0.0853 = 8.53%

CV_{cor} = 8.53 × {1 + (1 / 4 × 5)} = 8.70%

### Intra- and inter-assay coefficients of variations

#### Worked example

**Cow** No. | **PCV** | s_{i}^{2} | Mean | CV | CV^{2} |
1. | 2. |
1 | 33 | 35 | 2 | 34 | 0.042 | .002 |
2 | 26 | 23 | 4.5 | 24.5 | 0.087 | .007 |
3 | 29 | 29 | 0 | 29 | 0 | .000 |
4 | 32 | 35 | 4.5 | 33.5 | .063 | .004 |
5 | 31 | 28 | 4.5 | 29.5 | .072 | .005 |
6 | 31 | 31 | 0 | 31 | 0 | .000 |
7 | 31 | 34 | 4.5 | 32.5 | .065 | .004 |
8 | 31 | 29 | 2 | 30 | .047 | .002 |
9 | 35 | 33 | 2 | 34 | .042 | .002 |
10 | 21 | 24 | 4.5 | 22.5 | .094 | .009 |
Mean |
| | **2.85** | **30.05** | | **.00355** |
| |

Let's return to the example of two repeated measurements of packed cell volume that we used to demonstrate calculation of the within-subject standard deviation.

By using the root mean square approach:

Within-subject coefficient of variation = (√0.00355) × 100 = **5.96%**

By dividing the within assay standard deviation

by the overall mean:

Within-subject coefficient of variation = ((√2.85) / 30.05) × 100 = **5.62%**

The between-subject coefficient of variation is obtained from the variance of the means of the duplicate observations.

Hence between-subject coefficient of variation =
√(2 × 15.47) / 30.05 = **18.5%**