Q. 3.203 - 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 $1,2,4,4$

Step-by-Step Solution

Answer

(a) Population Mean$\left(\mu \right)$=$2.75$

(b) Population Standard deviation$\left(\sigma \right)$= $1.299$

Part(a) Step 1: Given Information

We are given simple data set of $1,2,4,4$

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

$\mu =\frac{1+2+4+4}{4}=\frac{11}{4}=2.75$

Hence, mean of given data is $2.75$ 

Part (b) Step 1:Given Information

We are provided simple data having $1,2,4,4$

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 

${\left(\sigma \right)}^2=\frac{(x}{}$₁-μ)²+............+(x_N-μ)²N

Where $x_i$ denotes $i_{th}$ value

$\mu$ denotes population mean

$N$ denotes total population

Using above formula,

$$\begin{gathered} \sigma =\sqrt{\frac{{(1-2.75)}^2+{(2-2.75)}^2+{(4-2.75)}^2+{(4-2.75)}^2}{4}} \\ =\sqrt{1.688} \\ =1.299 \end{gathered}$$

Hence, population standard deviation of given data is $1.299$