Questions: The coefficient of variation CV describes the standard deviation as a percent of the mean. Because it has no units, you can use the coefficient of variation to compare data with different units. Find the coefficient of variation for each sample data set. What can you conclude? CV = (Standard deviation / Mean) * 100% Data table Heights Weights 76 228 80 217 65 207 76 165 68 227 67 217 76 209 70 180 67 183 74 173 79 225 78 183

Solution Steps

To find the coefficient of variation (CV) for the heights data set, we need to calculate the standard deviation and the mean of the heights. The CV is then calculated by dividing the standard deviation by the mean and multiplying by 100 to express it as a percentage. This will allow us to compare the variability of the heights relative to their mean.

The mean of the heights data set is calculated as follows: \[ \text{Mean} = \frac{76 + 80 + 65 + 76 + 68 + 67 + 76 + 70 + 67 + 74 + 79 + 78}{12} = 73.0 \]

The standard deviation of the heights data set is calculated using the formula for sample standard deviation: \[ \text{Standard Deviation} = \sqrt{\frac{\sum (x_i - \text{Mean})^2}{n-1}} \] where \( n = 12 \) is the number of data points. The calculated standard deviation is: \[ \text{Standard Deviation} \approx 5.2915 \]

The coefficient of variation (CV) is calculated using the formula: \[ CV = \frac{\text{Standard Deviation}}{\text{Mean}} \times 100\% \] Substituting the values we have: \[ CV = \frac{5.2915}{73.0} \times 100\% \approx 7.2486\% \]

The CV is rounded to the nearest tenth: \[ CV \approx 7.2\% \]

Final Answer