The coefficient of variation is a measure of dispersion that tells us about the “spread” of our data. It tells us whether there is a high variation with the given data values or not. The higher the coefficient of variation the higher is the spread of the data values.

If a given data set has a high coefficient of variation then we say the data is less consistent. For example, suppose we collect the data about the number of hours a student studies per day for a hundred days. If the variation is high that would mean the student is not consistent in the number of hours he spends studying each day.

**Formula for calculating the Coefficient of Variation**:

We see that the coefficient of variation is the ratio between the standard deviation and the mean expressed in percentage.

**Steps to calculate Coefficient of Variation for given Data**:

- Calculate the mean of the data using the formula \bar{x} = \frac{\sum x_i}{n} where x
_{i }denotes the sample values and n denotes the size of the sample. - Calculate the standard deviation using the formula, \sigma = \sqrt{\frac{\sum x_i^2-\frac{(\sum x_i)^2}{n}}{n}}
- Divide the standard deviation by the mean and multiply the result by 100 to get the required value.

**Example 1:**

Calculate the coefficient of variation for the given set of data:

5, 6, 9, 8, 12, 14

**Solution**: We calculate the coefficient of variation in three steps as shown below:

Hence there is a variation of 35.14% in the given data.

*Let us look at another example of calculating the coefficient of variation.*

**Example 2:**

Calculate the coefficient of variation for the given set of data:

35, 54, 52, 53, 56, 58, 52, 50, 51, 49

**Solution**: * Step 1*: We first calculate the mean of the data using the formula,

x̄ = ∑x_{i }/n = 510/10 = 51

*Step 2*: Then we calculate the standard deviation using the formula,

Standard Deviation σ =√35 = 5.916

*Step *3: Coefficient of Variation(C.V) = Mean/Standard Deviation *100 = 11.6%

Hence there is a variation of 11.6% in the given data.