Answer to Question #329538 in Statistics and Probability for Grace

Question

 A population consists of the five measurements 2, 6, 8, 0, and 1.

1. What is the mean and the standard deviation of the population? 

Answer 1

1. Mean

$$\mu=\dfrac{2+6+8+0+1}{5}=3.4$$

Variance

$$\sigma^2=\dfrac{1}{5}\big((2-3.4)^2+(6-2.4)^2+(8-3.4)^2$$ $$(0-3.4)^2+(1-3.4)^2\big)=9.44$$

Standard deviation

$$\sigma=\sqrt{\sigma^2}=\sqrt{9.44}\approx3.0725$$