>>Return to Tell Me About Statistics!
The coefficient of variation is an indicator of variability. Usually, the indicators that express the variation that we use are mostly “standard deviation” and “dispersion.” This may be because there are few occasions when one requires a coefficient of variation when looking at the data. The coefficient of variation (CV) is a useful statistical tool. Knowledge of the coefficient of variation can reveal several aspects.
In this study, we will explain the coefficient of variation.
Coefficient of variation
The standard deviation divided by the mean is referred to as the coefficient of variation. The coefficient of variation is a dimensionless number that expresses relative variability.
It is used to compare variations in populations with different mean values, such as male and female heights, or different data units, such as height (cm) and weight (kg).
Formula for coefficient of variation
[Formula]
Coefficient of variation = standard deviation / average
A health checkup center decided to introduce a new digital height and weight scale. After measuring the height and weight of some staff members, before using it for examination, the data in the table below were obtained. Find the coefficients of variation for height and weight.
[Table]
Calculate height and weight by applying the formula above.
Coefficient of variation for height: 96÷160＝0.6
Coefficient of variation for weight: 55÷50 = 1.1
It is important not to misunderstand that a large standard deviation indicates a large variation.
Standard deviations with different units, such as height (cm) and weight (kg), cannot be judged as large or small based on their numerical values.
Notes on the coefficient of variation
As shown in the above example, the coefficient of variation has no units.
This is an important finding. IF the data with different or even the same units, the comparison of the standard deviation of data with different mean values is meaningless. In such cases, the coefficient of variation plays an important role. Without units, any scale or unit would be comparable.
There is no statistical criterion for how much the coefficient of variation should be, but it can be said that a coefficient of variation of 1 or more is “large,” and a coefficient of variation of 0.5 to 1 is “somewhat large.”
>>Return to Tell Me About Statistics!
Comments are closed