Question

In Exercises $3.65-3.70$, we have provided simple data sets for you to practice the basics of finding measures of variation . For each data set determine.

a) Range

b) sample standard deviation

$1,9,8,4,3$

Short answer

$$\begin{gathered} a)Range=8 \\ b)samples\tan darddeviation= \end{gathered}$$$3.39$

Step-by-step solution

Step 1. Given information. 

We have given data : 1,9,8,4,3

Step 2. Range of the data.   

$$\begin{gathered} Range=Max.value-Min.value \\ Range=9-1 \\ Range=8 \end{gathered}$$

Step 3. Mean  of the data.   

$$\begin{gathered} s=\sqrt{\frac{{\displaystyle \sum _{}\{x-\overline{x}{)}^2}}{n-1}} \\ Mean,\overline{x}=\frac{{\displaystyle \sum _{}x}}{n} \\ Mean=\frac{1+9+8+4+3}{5} \\ Mean=\frac{25}{5} \\ Mean=5 \\ sampiesize,n=5 \end{gathered}$$

Step 4. Standard deviation of the data. 

Variable $x$	Deviation from mean $x-\overline{x}$	Squared deviation ${\left(x-\overline{x}\right)}^2$
$$\begin{gathered} 1 \\ 9 \\ 8 \\ 4 \\ 3 \end{gathered}$$	$$\begin{gathered} -4 \\ 4 \\ 3 \\ -1 \\ -2 \end{gathered}$$	$$\begin{gathered} 16 \\ 16 \\ 9 \\ 1 \\ 4 \\ 46 \end{gathered}$$

Thus, the standard deviation is

$$\begin{gathered} s=\sqrt{\frac{{\displaystyle \sum _{}}{\left(x-\overline{x}\right)}^2}{n-1}} \\ =\sqrt{\frac{46}{5-1}} \\ =\sqrt{11.5} \\ =3.39 \end{gathered}$$