116 Chapter 3 Numerical Summaries of Data DEFINITION The coefficient of variation is found by dividing the standard deviation by the mean. CV = σ μ EXAMPLE 3.21 Computing the coefficient of variation NationalWeather Service records show that over a 30-year period, the annual precipitation in Atlanta, Georgia, had a mean of 49.8 inches with a standard deviation of 7.6 inches, and the annual temperature had a mean of 62.2 degrees Fahrenheit with a standard deviation of 1.3 degrees. Compute the coefficient of variation for precipitation and for temperature. Which has greater spread relative to its mean? Solution The coefficient of variation for precipitation is CV for precipitation = Standard deviation of precipitation Mean precipitation = 7.6 49.8 = 0.153 The coefficient of variation for temperature is CV for temperature = Standard deviation of temperature Mean temperature = 1.3 62.2 = 0.021 The CV for precipitation is larger than the CV for temperature. Therefore, precipitation has a greater spread relative to its mean. Note that we cannot compare the standard deviations of precipitation and temperature because they have different units. It does not make sense to ask whether 7.6 inches is greater than 1.3 degrees. The CV is unitless, however, so we can compare the CVs. Check Your Understanding 8. Lengths of newborn babies have a mean of 20.1 inches with a standard deviation of 1.9 inches. Find the coefficient of variation of newborn lengths. Answer is on page 123. USING TECHNOLOGY TI-84 Plus Computing the sample standard deviation The TI-84 PLUS procedure to compute the mean and median, described on page 96, will also compute the standard deviation. MINITAB Computing the sample standard deviation The MINITAB procedure to compute the mean and median, described on page 96, will also compute the standard deviation. EXCEL Computing the sample standard deviation The EXCEL procedure to compute the mean and median, described on page 96, will also compute the standard deviation.
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