The standard deviation is absolute measure of dispersion and hence can not be used for comparing variability of data sets with different means.
Therefore such comparisions are done by using a relative measure of dispersion called coefficient of variation(CV)
CV=\[\frac{x}{y}\]
where x is standard deviation and y is mean of the data set.
CV is also represented as a percentage CV % =\[\frac{x}{y}\] 100
when comparing data sets the data sets with larger vauue of CV % is more variable(less consistent) as compared to data set with lesser value of CV %.
For example.
|
y |
x |
CV% |
| Data set 1 |
5 |
1 |
20% |
| data set 2 |
20 |
2 |
10% |
although x=2 for dsta set 2 than y=1 , data set 2 is less variable than data set 1 , as it can be seen from the fact that data set 2 has CV% of 10% , while data set 1 has CV % of 20%.
So comparision of variability between 2 or more data set (with different means) should be done by comparing CV% and not by comparing standard deviations.
Example. If the standard deviation of the spot speed of the vehicle in a highway is 8.8 KMPH and mean speed of the vehicle is 33 KMPH ,the coefficient of variation in speed is
Solution
CV = \[\frac{x}{y}\]=\[\frac{8.8}{33}=0.2666\]
