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# Coefficient of variation  ### 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%

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

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

#### Worked example

 CowNo. PCV si2 Mean CV CV2 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%

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