Coefficient of Variation

The coefficient of variation (CV) expresses standard deviation as a percentage of the mean and is calculated as follows:

for population data
for sample data

Example 4.3:

The yearly salaries of all employees working for a company has a mean of MWK42350 and a standard deviation of MWK3820. The years of schooling for the same employees have a mean of 15 years and a standard deviation of 2 years. Is the relative variation in the salaries higher or lower than those in years of schooling for these employees?

Solution

Because the two variables have different units of measurement, we cannot compare the two standard deviations. Hence we calculate the coefficient of variation for each data set.

CV for salaries
CV for years of schooling

Since the CV for salaries has a lower value that the CV for years of schooling, the salaries have a lower relative spread that the years of schooling.

EXERCISES:

1. The texts cover the use of standard deviation by discussing the Chebyshev’s theorem and the empirical rule both of which demonstrate the uses of the standard deviation. Find out what are these.

2. The texts also cover measures of location. Discuss these measures of location.

3. The mean weight of a consignment of boxes is 25kg with a standard deviation of 4 kg. How could you describe the weights of the boxes?

4. The following table gives the distribution of gross weekly earnings for workers in a particular company.

Compare the distribution of weekly earnings for male and female workers by choosing and computing appropriate measures.

Income (MWK)
Males %
Females %
Less than 50
0.1
1.1
50 and < 60
0.1
2.3
60 and < 70
0.5
6.2
70 and < 80
1.0
10.8
80 and < 90
2.2
13.8
90 and < 100
3.4
14.1
100 and < 110
4.8
11.9
110 and < 120
5.7
10.4
120 and < 130
6.9
8.7
130 and < 150
15.0
10.2
150 and < 170
14.8
5.0
170 and < 200
17.7
3.5
200 and < 250
17.0
1.5
250 and < 300
6.6
0.4
300 or more
4.2
0.1