Question

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% click the icon to view the data sets. cv heights = % (round to the nearest tenth as needed.) data table heights 73 68 79 71 77 74 69 68 75 65 67 72 weights 217 197 222 229 179 227 225 211 177 180 195 224

Explanation:

Step1: Calculate the mean of heights

Let the height - data set be \(x_1,x_2,\cdots,x_n\). The number of data points \(n = 12\). The sum of the height values \(S=\sum_{i = 1}^{12}x_i=72 + 67+65 + 75+68+69+74+77+71+79+68+73=848\). The mean \(\bar{x}=\frac{S}{n}=\frac{848}{12}\approx70.7\).

Step2: Calculate the standard - deviation of heights

The formula for the sample standard deviation \(s=\sqrt{\frac{\sum_{i = 1}^{n}(x_i-\bar{x})^2}{n - 1}}\).
\((72 - 70.7)^2=1.69\), \((67 - 70.7)^2 = 13.69\), \((65 - 70.7)^2=32.49\), \((75 - 70.7)^2 = 18.49\), \((68 - 70.7)^2=7.29\), \((69 - 70.7)^2 = 2.89\), \((74 - 70.7)^2=10.89\), \((77 - 70.7)^2 = 39.69\), \((71 - 70.7)^2=0.09\), \((79 - 70.7)^2 = 68.89\), \((68 - 70.7)^2=7.29\), \((73 - 70.7)^2 = 5.29\).
The sum \(\sum_{i = 1}^{12}(x_i - 70.7)^2=1.69+13.69+32.49+18.49+7.29+2.89+10.89+39.69+0.09+68.89+7.29+5.29 = 208.2\).
\(s=\sqrt{\frac{208.2}{11}}\approx4.34\).

Step3: Calculate the coefficient of variation of heights

The formula for the coefficient of variation \(CV=\frac{s}{\bar{x}}\times100\%\).
\(CV=\frac{4.34}{70.7}\times100\%\approx6.1\%\).

Answer:

6.1%