Question

Find the sample variance and the standard deviation for the following sample. Round the answers to at least two decimal places as needed. 16 30 20 18 13

Answer 1

Answer:

The sample variance is 41.8

The standard deviation is 6.465

Explanation:

Given: $\text{n}=5$

Formulas used:

$\begin{aligned}\text{Sample Mean} \;\left(\text{X} \right )&=\frac{\sum X}{\text{n}}\\\text{Sample Variance}\;\left(\text{S}^2 \right )&=\frac{\sum \left(\text{Xi-X} \right )^2}{\text{n}-1}\\\text{Sample Standard Deviation}&=\sqrt{\text{S}^2}\\\end{aligned}$

Computation:

$\begin{aligned}\text{Sample Mean} \;\left(\text{X} \right )&=\frac{16+30+20+18+13}{5}\\&=19.4\\\text{Sample Variance}\;\left(\text{S}^2 \right )&=\frac{\left(16-19.4 \right )^2+\left(30-19.4 \right )^2+\left(20-19.4 \right )^2+\left(18-19.4 \right )^2+\left(13-19.4 \right )^2}{5-1}\\&=41.8\\\text{Standard Deviation}&=\sqrt{41.8}\\&=6.465\\\end{aligned}$