Question

Consider the following sets of sample data:A: $29,900, $29,200, $26,100, $39,300, $24,200, $37,300, $34,300, $29,700, $35,100, $21,100, $38,800, $25,100, $27,200, $29,100B: 3.42, 3.53, 4.41, 3.95, 3.18, 4.85.3.13, 4.23,3.53, 4.72, 3.24Step 1 of 2: For each of the above sets of sample data, calculate the coefficient of variation, CV. Round to one decimal place.

Answer 1

Answer:

The coefficient of variance is 0.2

Explanation:

The coefficient of variance is given as:

$\begin{gathered} CV=\frac{\sigma}{\mu} \\ \\ \sigma\text{ - Standard deviation} \\ \mu\text{ - Mean} \end{gathered}$

We find the mean and standard deviation first.

Part A:

Mean:

$\begin{gathered} \mu=\sum ^{14}_{i\mathop=1}\frac{x_i}{14} \\ \\ =\frac{416400}{14}=29742.9 \end{gathered}$

Standard Deviation:

$\begin{gathered} \sigma=\sqrt[]{\sum ^{14}_{i\mathop{=}1}\frac{(x_i-\mu)^2}{14}} \\ \\ =\sqrt[]{\frac{339562784.9}{14}} \\ \\ =\sqrt[]{24254484.64} \\ \\ =4924.9 \end{gathered}$

Therefore, the coefficient of variance is:

$\frac{4924.9}{29742.9}=0.2$