I'm reviewing right now for an exam and I've stumbled across this online reviewer. In the solution for question #2 it stated that Section B is more consistent so there is greater variability in the wages of section A.
Coefficient of variance for Section A = 7/450 x 100 =1.56 %
Coefficient of variance for Section B = 9/350 x 100 = 2.57%
My answer is the opposite, that section B is less consistent and there is less variability in section A. Am I correct or did I misunderstand something?
The sample coefficient of variation is the sample standard deviation divided by the sample mean.
Here is an illustration: Which has greater variability, weights of elephants or weights of ants. In terms of the standard deviation the answer has to be elephants because they weigh more. Dividing by the mean tends to put the two measures of variability on the 'same scale'. In terms of the coefficient of variation, the answer is probably ants. Some species of ants are several times larger than others. So relative to their small size, ants may be considered more variable.
Put in another way, the sample SD and sample mean have the same units. This means the coefficient of variation (CV) is a 'dimensionless' measure of variability. So even if elephants are weighed in tons and ants in grams, the CVs have no units and can be compared directly. (You might want to read parts of the Wikipedia article on 'coefficient of variation'.)
Finally, I wonder how you are computing the CV in your example. Could you be confusing the variance and the SD?