The standard deviation alone does not measure relative variation. For example, a standard deviation of $1 would be considered large if it is describing the variability from store to store in the price of an ice cube tray. On the other hand, a standard deviation of $1 would be considered small if it is describing store-to-store variability in the price of a particular brand of freezer. A quantity designed to give a relative measure of variability is the coefficient of variation. Denoted by CV, the coefficient of variation expresses the standard deviation as a percentage of the mean. It is defined by the formula CV = 100(s/x bar). Consider two samples. Sample 1 gives the actual weight (in ounces) of the contents of cans of pet food labeled as having a net weight of 8 oz. Sample 2 gives the actual weight (in pounds) of the contents of bags of dry pet food labeled as having a net weight of 50 lb. There are weights for the two samples.
Sample 1 7.8 6.2 6.1 7.8 6.1
7.8 7.5 6.3 6.3 6.5
Sample 2 51.5 51.6 51 51.8 50.7
47 50.4 50.3 48.7 48.2
(a) For each of the given samples, calculate the mean and the standard deviation. (Round all intermediate calculations and answers to five decimal places.)
For sample 1
Mean Standard deviation For sample 2
Mean Standard deviation (b) Compute the coefficient of variation for each sample. (Round all answers to two decimal places.)
CV1 CV2