Notes pg52-63

# Notes pg52-63 - 52 Coefficient of Variation The coefficient...

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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. As a rule of thumb, values greater than 1.0 indicate high levels of risk and those less than 1.0 indicate low levels of risk. It is a measure of risk or uncertainty that is often used in finance and insurance. Since the coefficient of variation is “unitless”, it can be used to compare data sets that are in different units. Example 1 (case where CV is calculated to compare two variables measured in the same units) : 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? 52

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Example 2 (comparing two data sets measured in different units) : An HR director for a large manufacturing plant would like to analyze the relationship between education level of employees (measured in year of formal education after high school) and annual salary (in \$1000s). To begin her analysis she calculates the mean and variance for both variables and finds that: mean annual income = \$78,000 standard deviation of annual income=\$11,000 CV for income = mean number of years of post H.S. education = 1.5 years standard deviation of post H.S. education = 2.0 years CV for years of formal education = Conclusions? 53
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 Frequency 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: mean > median > mode. 0 1 2 3 4 5 6 7 8 Frequenc 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 54

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median. Common examples of right-skewed data are incomes and home sale prices. Negatively skewed data. Mean < median <model. 0 1 2 3 4 5 6 7 Frequency The above data set is leftward, or negatively skewed. In this case, the mean is to the left of the median.
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Notes pg52-63 - 52 Coefficient of Variation The coefficient...

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