he 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 7.4 6.8 6.7 7.2 6.7 7.4 7.3 6.5 6.5 6.4 Sample 2 50.5 52.7 50.6 51.4 50.9 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 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

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.4: Distributions Of Data

Problem 19PFA

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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	7.4	6.8	6.7	7.2	6.7
7.4	7.3	6.5	6.5	6.4
Sample 2	50.5	52.7	50.6	51.4	50.9
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 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

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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