Question
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
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 thecoefficient of variation. Denoted by CV, the coefficient of variation expresses the standard deviation as a percentage of the mean. It is defined by the following formula.
CV= 100(s/x)
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 of8 ounces.Sample 2gives the actual weight (in pounds) of the contents of bags of dry pet food labeled as having a net weight of50 pounds.The weights for the two samples are as follows.
Sample 1 | 6.5 | 5.3 | 5.1 | 6.6 | 5.1 |
---|---|---|---|---|---|
6.5 | 6.2 | 5.2 | 5.2 | 5.2 | |
Sample 2 | 52.1 | 50.7 | 50.8 | 51.6 | 52.6 |
47.0 | 50.4 | 50.3 | 48.7 | 48.2 |
(a)For each of the given samples, calculate the mean and the standard deviation. (Round your standard deviations to four decimal places.)Sample 1Mean Standard Deviation Sample 2Mean Standard Deviation (b)Calculate the coefficient of variation for each sample. (Round your answers to two decimal places.)CV1CV2
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