1) The average playing time of compact discs in a large collection is 32 min, and the standard deviation is 4 min.
(a) What value is 1 standard deviation above the mean? 1 standard deviation below the mean? What values are 2 standard deviations away from the mean?
1 standard deviation above the mean | |
1 standard deviation below the mean | |
2 standard deviation above the mean | |
2 standard deviation below the mean |
2) 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 ). 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 | 8.7 | 7.6 | 7.5 | 8.8 | 7.5 |
8.7 | 8.3 | 7.2 | 7.2 | 7.5 | |
Sample 2 | 52.3 | 50.2 | 51.7 | 52.1 | 50.6 |
47 | 50.4 | 50.3 | 48.7 | 48.2 |
a)
For sample 2 | |
Mean | |
Standard deviation |
(b) Compute the coefficient of variation for each sample. (Round
all answers to two decimal places.)
CV_{1} | |
CV_{2} |
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