Answer :
To calculate the Coefficient of Variation (CV) for the given data, we need to follow these steps:
Calculate the Mean of the Data:
The mean is the average of all the data points.
[tex]\text{Mean} = \frac{160 + 170 + 164 + 163 + 164 + 163 + 162 + 163 + 161 + 160}{10} = \frac{1630}{10} = 163[/tex]
Calculate the Standard Deviation (SD) of the Data:
The standard deviation measures how much the data points tend to deviate from the mean.
First, calculate the sum of the squared deviations from the mean:
[tex]\begin{align*}
& (160 - 163)^2 + (170 - 163)^2 + (164 - 163)^2 + (163 - 163)^2 + (164 - 163)^2 \\
& + (163 - 163)^2 + (162 - 163)^2 + (163 - 163)^2 + (161 - 163)^2 + (160 - 163)^2
\end{align*}[/tex]Which equals:
[tex]9 + 49 + 1 + 0 + 1 + 0 + 1 + 0 + 4 + 9 = 74[/tex]
Now divide by the number of data points to get the variance, and then take the square root for the standard deviation:
[tex]\text{Variance} = \frac{74}{10} = 7.4[/tex]
[tex]\text{Standard Deviation} = \sqrt{7.4} \approx 2.72[/tex]
Calculate the Coefficient of Variation (CV):
The coefficient of variation is the ratio of the standard deviation to the mean, expressed as a percentage:
[tex]\text{CV} = \left( \frac{\text{Standard Deviation}}{\text{Mean}} \right) \times 100\%[/tex]
[tex]\text{CV} = \left( \frac{2.72}{163} \right) \times 100\% \approx 1.67\%[/tex]
Therefore, the Coefficient of Variation for the given data is approximately 1.67%.
