Question

prof: mr. nougues
course: probability and statistics
consider the data below, calculate the coefficient of variation for the heights and weight: use $sigma = 4.4$
heights; 72, 74, 68, 76, 74, 69, 72, 79, 70, 69, 77, 73,78
weight: 180, 168, 225, 201, 189, 192, 197, 162, 174, 171, 185, 210,220

Explanation:

Step1: Calculate mean of heights

First, sum up the height values: $72 + 74+68 + 76+74+69+72+79+70+69+77+73+78=931$. There are $n = 13$ data - points. The mean of heights $\bar{x}_{h}=\frac{931}{13}=71.62$.

Step2: Calculate coefficient of variation for heights

The coefficient of variation formula is $CV=\frac{\sigma}{\bar{x}}\times100\%$. Given $\sigma = 4.4$, for heights $CV_{h}=\frac{4.4}{71.62}\times100\%\approx6.14\%$.

Step3: Calculate mean of weights

Sum up the weight values: $180 + 168+225+201+189+192+197+162+174+171+185+210+220 = 2484$. There are $n = 13$ data - points. The mean of weights $\bar{x}_{w}=\frac{2484}{13}=191.08$.

Step4: Calculate coefficient of variation for weights

Using the coefficient of variation formula with $\sigma = 4.4$, for weights $CV_{w}=\frac{4.4}{191.08}\times100\%\approx2.30\%$.

Answer:

Coefficient of variation for heights is approximately $6.14\%$ and for weights is approximately $2.30\%$.