91Ó°ÊÓ

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

We need to find population mean of given data

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

Population Mean$\left(\mathrm{μ}\right)$=$\frac{\underset{}{∑}{x}_i}{N}$

$x_i$denotes individual value

$N$denotes total population

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

Hence, mean of given data is $5$

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

We need to find standard deviation of given population.

We know standard deviation is square root of variance.

Formula of variance is

${\mathrm{σ}}^2=\frac{{(x_1-\mathrm{μ})}^2+...........+{(x_N-\mathrm{μ})}^2}{N}$

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

$\mathrm{μ}$denotes population mean

$N$denotes total population

Using above formula, Standard deviation is

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

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