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. 38.5,33.4,33.6,39.5,39.3 show your work here i

Explanation:

Step1: Calculate the mean

The mean $\mu$ of a data - set $x_1,x_2,\cdots,x_n$ is given by $\mu=\frac{\sum_{i = 1}^{n}x_i}{n}$. Here, $n = 5$, $x_1=38.5$, $x_2 = 33.4$, $x_3=33.6$, $x_4=39.5$, $x_5=39.3$.
$\mu=\frac{38.5 + 33.4+33.6+39.5+39.3}{5}=\frac{184.3}{5}=36.86$

Step2: Calculate the population standard deviation $\sigma$

The formula for the population standard deviation is $\sigma=\sqrt{\frac{\sum_{i = 1}^{n}(x_i-\mu)^2}{n}}$.
$(x_1 - \mu)^2=(38.5 - 36.86)^2=(1.64)^2 = 2.6896$
$(x_2-\mu)^2=(33.4 - 36.86)^2=(-3.46)^2 = 11.9716$
$(x_3-\mu)^2=(33.6 - 36.86)^2=(-3.26)^2 = 10.6276$
$(x_4-\mu)^2=(39.5 - 36.86)^2=(2.64)^2 = 6.9696$
$(x_5-\mu)^2=(39.3 - 36.86)^2=(2.44)^2 = 5.9536$
$\sum_{i = 1}^{5}(x_i-\mu)^2=2.6896 + 11.9716+10.6276+6.9696+5.9536=38.212$
$\sigma=\sqrt{\frac{38.212}{5}}=\sqrt{7.6424}\approx2.7645$

Step3: Calculate the coefficient of variation (CV)

The coefficient of variation is given by $CV=\frac{\sigma}{\mu}\times100\%$.
$CV=\frac{2.7645}{36.86}\times100\%\approx7.49\%$

Answer:

$7.49\%$