Answer :
To compare the variability of height with that of weight for a group of employees, we can use the coefficient of variation (CV). The coefficient of variation is a standardized measure of dispersion or variability within a data set, expressed as a percentage. It is calculated as the ratio of the standard deviation (SD) to the mean, and it allows us to compare the variability of two different data sets, even if they have different units or scales.
Let's calculate the coefficient of variation for both height and weight:
Coefficient of Variation for Height:
- Mean height [tex]\mu_{\text{height}} = 172 \text{ cm}[/tex]
- Standard deviation of height [tex]\sigma_{\text{height}} = 18 \text{ cm}[/tex]
[tex]CV_{\text{height}} = \left( \frac{\sigma_{\text{height}}}{\mu_{\text{height}}} \right) \times 100 = \left( \frac{18}{172} \right) \times 100 \approx 10.47\%[/tex]
Coefficient of Variation for Weight:
- Mean weight [tex]\mu_{\text{weight}} = 65 \text{ kg}[/tex]
- Standard deviation of weight [tex]\sigma_{\text{weight}} = 9 \text{ kg}[/tex]
[tex]CV_{\text{weight}} = \left( \frac{\sigma_{\text{weight}}}{\mu_{\text{weight}}} \right) \times 100 = \left( \frac{9}{65} \right) \times 100 \approx 13.85\%[/tex]
Comparison of Variability:
- The coefficient of variation for height is approximately [tex]10.47\%[/tex].
- The coefficient of variation for weight is approximately [tex]13.85\%[/tex].
Since the coefficient of variation for weight is higher than that for height, this indicates that there is more relative variability in the weights of the employees compared to their heights, even though the absolute standard deviation of weight is lower than that of height.
