Question

We have provided simple data for you to practice the basics of finding:

(a) Population mean

(b) Population standard deviation

Data is$4,0,5$

Short answer

(a) Population Mean$\left(\mu \right)$=$3$

(b) Population Standard deviation$\left(\sigma \right)$=$2.16$

Step-by-step solution

Part(a) Step 1: Given information 

We are given simple data set of $4,0,5$

We need to find population mean of given data

Part(a) Step 2: Simplify 

A population in statistics is a group of similar items or events that relate to a query or experiment.

Population Mean$\left(\mu \right)$=$\underset{}{\sum x_i/N}$

$x_i$denotes individual value

$N$ denotes total population

$=\frac{4+0+5}{3}=3$

Hence, mean of given data is $3$.

Part (b) Step 1:Given Information

We are provided simple data having $4,0,5$

We need to find standard deviation of given population.

Part(b) Step 2:Simplify

We know standard deviation is square root of variance.

Variance$\left({\sigma }^2\right)$=$\frac{{(x_1-\mu )}^2+......+{(x_N-\mu )}^2}{N}$

Where $\mu$denotes population mean

$x_i$denotes $i_{th}$value

$N$denotes total number of population

$\sigma =\sqrt{\frac{{(4-3)}^2+{(0-3)}^2+{(5-3)}^2}{3}}=\sqrt{4.667}=2.16$

Hence, population standard deviation of given data is$2.16$.