Question

find the coefficient of variation percentage of the data set (as a population) below. round your answer to the nearest hundredths place if applicable. 29.3, 29.3, 31.9, 30.5, 28, 28.3 show your work here

Explanation:

Step1: Calculate the mean

The mean $\mu$ of a data - set $x_1,x_2,\cdots,x_n$ is $\mu=\frac{\sum_{i = 1}^{n}x_i}{n}$. Here, $n = 6$, $x_1=29.3,x_2 = 29.3,x_3=31.9,x_4=30.5,x_5=28,x_6=28.3$.
$\sum_{i=1}^{6}x_i=29.3 + 29.3+31.9+30.5+28+28.3=177.3$.
$\mu=\frac{177.3}{6}=29.55$.

Step2: Calculate the population standard deviation

The population standard deviation $\sigma=\sqrt{\frac{\sum_{i = 1}^{n}(x_i-\mu)^2}{n}}$.
$(29.3 - 29.55)^2=(-0.25)^2 = 0.0625$ (twice since there are two 29.3s).
$(31.9 - 29.55)^2=(2.35)^2 = 5.5225$.
$(30.5 - 29.55)^2=(0.95)^2 = 0.9025$.
$(28 - 29.55)^2=(-1.55)^2 = 2.4025$.
$(28.3 - 29.55)^2=(-1.25)^2 = 1.5625$.
$\sum_{i = 1}^{6}(x_i - 29.55)^2=2\times0.0625+5.5225 + 0.9025+2.4025+1.5625=10.515$.
$\sigma=\sqrt{\frac{10.515}{6}}\approx\sqrt{1.7525}\approx1.3238$.

Step3: Calculate the coefficient of variation

The coefficient of variation $CV=\frac{\sigma}{\mu}\times100\%$.
$CV=\frac{1.3238}{29.55}\times100\%\approx4.48\%$.

Answer:

$4.48\%$