Question

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

(a) Population mean

(b) Population standard deviation

Data is$1,9,8,4,3$

Short answer

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

(b) Population Standard deviation$\left(\sigma \right)$= $3.033$

Step-by-step solution

Part(a) Step 1: Given information 

We are given simple data set of$1,9,8,4,3$

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$\left(\mu \right)$=$\frac{\sum _{}{x}_i}{N}$

$x_i$denotes individual value

$N$denotes total population

$$\begin{gathered} \mu =\frac{1+9+8+4+3}{5} \\ \mu =\frac{25}{5}=5 \end{gathered}$$

Hence, mean of given data is $5$

Part (b) Step 1:Given Information

We are provided simple data having$1,9,8,4,3$

We need to find standard deviation of given population.

Part(b) Step 2: Simplify

We know standard deviation is square root of variance.

Formula of variance is

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

Where $x_i$denotes $i_{th}$value

$\mu$denotes population mean

$N$denotes total population

Using above formula, Standard deviation is

$$\begin{gathered} \sigma =\sqrt{\frac{{(1-5)}^2+{(9-5)}^2+{(8-5)}^2+{(4-5)}^2+{(3-5)}^2}{5}} \\ =\sqrt{\frac{4^2+4^2+3^2+1^2+2^2}{5}} \\ =3.033 \end{gathered}$$

Hence, population standard deviation of given data is$3.033$