What is Coefficient of Variation?

The coefficient of variation (CV) is a statistical measure used to determine the relative variability of a dataset. It is particularly useful when comparing the variability between datasets that have different units of measurement or different scales. The CV is expressed as a percentage and is calculated by dividing the standard deviation of the dataset by the mean and multiplying by 100.

Calculating the Coefficient of Variation:

The formula to calculate the coefficient of variation is as follows:

CV = (Standard Deviation / Mean) * 100

In order to calculate the coefficient of variation, we need to know the standard deviation and the mean of the dataset.

Given Data:
- Variance = 12
- Mean = 40

Calculating the Standard Deviation:

The variance is the square of the standard deviation. Therefore, to calculate the standard deviation, we need to take the square root of the variance.

Standard Deviation = √Variance = √12 = 3.464

Calculating the Coefficient of Variation:

Now that we have the standard deviation and the mean, we can calculate the coefficient of variation using the formula mentioned earlier.

CV = (Standard Deviation / Mean) * 100 = (3.464 / 40) * 100 = 8.66

Therefore, the coefficient of variation for the given dataset is 8.66%.

Interpreting the Coefficient of Variation:

The coefficient of variation is a measure of relative variability. It allows us to compare the variability of datasets with different units or scales.

In this case, the coefficient of variation is 8.66%, which indicates that the dataset has a relatively low level of variability compared to the mean. A lower coefficient of variation suggests that the data points are closer to the mean, indicating less dispersion.

The coefficient of variation is particularly useful in fields such as finance, where it is used to compare the risk or volatility of different investments. A higher coefficient of variation implies a greater level of risk or volatility.

In summary, the coefficient of variation is a statistical measure that allows us to compare the relative variability of datasets. It is calculated by dividing the standard deviation by the mean and multiplying by 100. In this case, the coefficient of variation for the given dataset is 8.66%.