Q. 3.201 - Elementary Statistics

Question

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

(a) Population mean

(b) Population standard deviation

Data is $4,0,5$

Step-by-Step Solution

Answer

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

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

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 $2.16$.