pp.51-66mgsc 291 fall 2009

# pp.51-66mgsc 291 fall 2009 - 51 Coefficient of Variation...

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Coefficient of Variation The coefficient of variation is calculated as: standard deviation CV= ×100 % mean . It is a measure of the standard deviation relative to the mean. As such it is a relative measure of risk. In general, values greater than 1.0 are considered to have large standard deviations, those less than 1.0 have relatively low standard deviations. It is a measure of risk or uncertainty of a variable and is used often in finance and insurance. It can be used to compare data sets that are in the same units and is also useful when comparing two data sets that have different units. Example : Consider two stocks, A and B. Stock A has a mean ROR of 5% and a standard deviation which is also 5%. Stock B has a rate of return of 10% and a standard deviation of 7%. Which stock is more variable? Which stock is riskier? 51

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Example : A consumer electronics store sells cell phones. They would like to know whether the amount of money a customer spends on a cell phone appears to be sensitive to his or her income. Suppose they only know the mean and standard deviations of each variable. Based on the statistics below, does it appear that the amount spent on a cell phone is sensitive to customer income? Customer : mean annual income = \$40,000 standard deviation of annual income=\$40,000 mean amount spent on a cell phone = \$125 standard deviation for amount spent on a cell phone = \$25. 52
Relative Positions of the Mean, Median, and Mode Symmetric data. The mean and median are the same. 0 1 2 3 4 5 6 7 8 9 10 Frequenc When the data are symmetric, the mean and median are the same. For this data set, the mode is also equal to the mean and median. Positively skewed data, the mean is greater than the median. 0 1 2 3 4 5 6 7 8 Frequen The above data set is not symmetric, it is ‘skewed’. If you tried to draw a smooth curve for this distribution, the ‘tail’ of the distribution would be on the right side. The data is skewed to the right, or positively skewed. For right-skewed data, the mean is greater than the median. Common examples of right-skewed data are incomes and home sale prices. 53

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Negatively skewed data. The mean is less than the median. 0 1 2 3 4 5 6 7 Frequency The above data set is leftward, or negatively skewed.
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