Q. 3.202 - Elementary Statistics

Question

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

(a) Population mean

(b) Population standard deviation

Data is $3,5,7$

Step-by-Step Solution

Answer

(a) Population Mean$\left(\mu \right)$=$5$

(b) Population Standard deviation$\left(\sigma \right)$= $1.663$

Part(a) Step 1: Given information

We are given simple data set of $3,5,7$

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$\left(\mu \right)$=$\frac{\underset{}{\sum x_i}}{N}$

$x_i$ denotes individual value

$N$ denotes total population

$\mu =\frac{3+5+7}{3}$

Hence, mean of given data is $5$. 

Part (b) Step 1:Given Information

We are provided simple data having $3,5,7$

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 $x_i$ denotes $i_{th}$ value

$\mu$  denotes population mean

$N$ denotes total population

Using above formula,

$$\begin{gathered} \sigma =\sqrt{\frac{{(5-3)}^2+{(5-5)}^2+{(5-7)}^2}{3}} \\ =\sqrt{2.667} \\ =1.663 \end{gathered}$$

Hence, population standard deviation of given sample data is $1.663$