Question

The 5 participants in a weight-loss class lost the following weights (in pounds) after three weeks of dieting.1, 4, 3, 1, 6Send data to calculatorAssuming that these weights constitute an entire population, find the standard deviation of the population. Round your answer to two decimal places.(If necessary, consult a list of formulas.)05

Answer 1

Given:

The data 1, 4, 3, 1, 6.

Required:

Find standard deviation.

Explanation:

Formula to calculate standard deviation,

$\begin{gathered} \sigma=\sqrt{\frac{\sum_{i\mathop{=}1}^N(x_i-\mu)^2}{N}} \\ Where, \\ \sigma(\text{ standard deviation}) \\ x_i(\text{ Values from dataset}) \\ \mu(Mean) \\ N(\text{ Total count of dataset}) \end{gathered}$

First the mean,

$\begin{gathered} Mean(\mu)=\frac{1+4+3+1+6}{5} \\ \mu=\frac{15}{5} \\ \mu=3 \end{gathered}$

Now,

$\begin{gathered} \sigma=\sqrt{\frac{(1-3)^2+(4-3)^2+(3-3)^2+(1-3)^2+(6-3)^2}{5}} \\ \sigma=\sqrt{\frac{18}{5}} \\ \sigma=\sqrt{3.6} \\ \sigma=1.90 \end{gathered}$

Answer:

Standard deviation equals 1.90