To calculate the coefficient of variation, we need to first find the standard deviation and mean of the given numbers.



To find the mean, we need to add up all the numbers and divide by the total count of numbers.

5 + 1 + 8 + 7 + 2 = 23

23/5 = 4.6

Therefore, the mean of the given numbers is 4.6.



To find the standard deviation, we need to first find the deviation of each number from the mean.

5 - 4.6 = 0.4
1 - 4.6 = -3.6
8 - 4.6 = 3.4
7 - 4.6 = 2.4
2 - 4.6 = -2.6

Next, we need to square each deviation.

0.4^2 = 0.16
(-3.6)^2 = 12.96
3.4^2 = 11.56
2.4^2 = 5.76
(-2.6)^2 = 6.76

Then we need to find the average of these squared deviations.

(0.16 + 12.96 + 11.56 + 5.76 + 6.76)/5 = 7.04

Finally, we take the square root of the average squared deviation to find the standard deviation.

√7.04 = 2.65

Therefore, the standard deviation of the given numbers is 2.65.



Now that we have found the mean and standard deviation, we can calculate the coefficient of variation using the formula:

Coefficient of Variation = (Standard Deviation / Mean) x 100%

(2.65 / 4.6) x 100% = 57.61%

Therefore, the coefficient of variation of the given numbers is 57.61%.



The coefficient of variation is a measure of relative variability. It shows the amount of variability relative to the mean. A high coefficient of variation indicates that the data has a high degree of variability relative to the mean, while a low coefficient of variation indicates that the data has a low degree of variability relative to the mean.

In this case, the coefficient of variation is 57.61%, which indicates that the given numbers have a relatively high degree of variability relative to the mean. It is important to note that the coefficient of variation is a dimensionless measure, meaning it does not have any units. This makes it useful for comparing variability between datasets with different units of measurement.