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 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 of 8 ounces. 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 pounds. The weights for the two samples are as follows. Sample 1 9.4 8.6 8.2 9.6 8.2 9.4 9.7 8.2 8.2 8.5 Sample 2 52.3 52.5 51.8 51.7 51.1 47 50.4 50.3 48.7 48.2 (a) For each of the given samples, calculate the mean and the standard deviation. (Round your answers to five decimal places.) Sample 1 MeanStandard DeviationSample 2 MeanStandard Deviation(b) Calculate the coefficient of variation for each sample. (Round your answers to two decimal places.) CV1CV2
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 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 of 8 ounces. 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 pounds. The weights for the two samples are as follows.
Sample 1
9.4
8.6
8.2
9.6
8.2
9.4
9.7
8.2
8.2
8.5
Sample 2
52.3
52.5
51.8
51.7
51.1
47
50.4
50.3
48.7
48.2
(a)
For each of the given samples, calculate the mean and the standard deviation. (Round your answers to five decimal places.)
Sample 1
Mean
Standard Deviation
Sample 2
Mean
Standard Deviation
(b)
Calculate the coefficient of variation for each sample. (Round your answers to two decimal places.)
CV1
CV2
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