Question

given the population, 20, 35, 55, 40, and 25, what is the standard deviation?
\\(\sigma = \sqrt{\frac{\sum (x - \mu)^2}{n}}\\)
(round off to two decimal places as they occur.)
5.92
6.63
12.25
13.71

Explanation:

Step1: Calculate mean $\mu$

$\mu=\frac{20 + 35+55+40+25}{5}=35$

Step2: Calculate $(x - \mu)^2$ values

$(20 - 35)^2=225$, $(35 - 35)^2 = 0$, $(55 - 35)^2=400$, $(40 - 35)^2 = 25$, $(25 - 35)^2=100$

Step3: Calculate $\sum(x - \mu)^2$

$\sum(x - \mu)^2=225+0 + 400+25+100 = 750$

Step4: Calculate standard - deviation $\sigma$

$\sigma=\sqrt{\frac{750}{5}}=\sqrt{150}\approx13.71$

Answer:

D. 13.71