the coefficient of variation cv describes the standard deviation as a percent variation for each sample data…

the coefficient of variation cv describes the standard deviation as a percent variation for each sample data set. what can you conclude? cv = \\frac{standard deviation}{mean} \\cdot 100% click the icon to view the data sets. cv_{heights} = % (round to the nearest tenth as needed.) data table heights weights 73 187 79 215 66 223 77 194 78 208 73 175 73 227 78 225 69 168 69 205 65 177 68 222

the coefficient of variation cv describes the standard deviation as a percent variation for each sample data set. what can you conclude? cv = \\frac{standard deviation}{mean} \\cdot 100% click the icon to view the data sets. cv_{heights} = % (round to the nearest tenth as needed.) data table heights weights 73 187 79 215 66 223 77 194 78 208 73 175 73 227 78 225 69 168 69 205 65 177 68 222

Answer

Explanation:

Step1: Calculate the mean of heights

The formula for the mean $\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}$. Here, $n = 12$, and $\sum_{i=1}^{12}x_{i}=73 + 79+66 + 77+78+73+73+78+69+69+65+68=859$. So, $\bar{x}=\frac{859}{12}\approx71.6$.

Step2: Calculate the standard - deviation of heights

The formula for the sample standard - deviation $s=\sqrt{\frac{\sum_{i = 1}^{n}(x_{i}-\bar{x})^{2}}{n - 1}}$. First, calculate $(x_{i}-\bar{x})^{2}$ for each $x_{i}$: $(73 - 71.6)^{2}=1.96$, $(79 - 71.6)^{2}=54.76$, $(66 - 71.6)^{2}=31.36$, $(77 - 71.6)^{2}=29.16$, $(78 - 71.6)^{2}=40.96$, $(73 - 71.6)^{2}=1.96$, $(73 - 71.6)^{2}=1.96$, $(78 - 71.6)^{2}=40.96$, $(69 - 71.6)^{2}=6.76$, $(69 - 71.6)^{2}=6.76$, $(65 - 71.6)^{2}=43.56$, $(68 - 71.6)^{2}=12.96$. $\sum_{i = 1}^{12}(x_{i}-\bar{x})^{2}=1.96+54.76+31.36+29.16+40.96+1.96+1.96+40.96+6.76+6.76+43.56+12.96 = 273.2$. Then, $s=\sqrt{\frac{273.2}{11}}\approx4.97$.

Step3: Calculate the coefficient of variation

Using the formula $CV=\frac{s}{\bar{x}}\times100%$, substitute $s\approx4.97$ and $\bar{x}\approx71.6$. So, $CV=\frac{4.97}{71.6}\times100%\approx6.9%$.

Answer:

$6.9$