Answer :
Explanation:
The set of numbers are given below as
[tex]7,1,7,10,5,3,2[/tex]Concept:
The formula for standard deviation is given below as
[tex]\begin{gathered} \sigma\left(X\right)=\sqrt{\frac{\sum_{i=1}^7\left(x_i-\bar{x}\right)^2}{n-1}} \\ where, \\ \bar{x}=mean \\ n=7 \end{gathered}[/tex]Step 1:
We will calculate the mean of the set of data
[tex]\begin{gathered} \bar{x}=\frac{sumofnumbers}{numberofdata}=\frac{7+1+7+10+5+3+2}{7} \\ \bar{x}=\frac{35}{7}=5 \end{gathered}[/tex]Step 2:
Calculate the mean deviation below
[tex]x-\bar{x}[/tex][tex]\begin{gathered} 7-5=2 \\ 1-5=-4 \\ 7-5=2 \\ 10-5=5 \\ 5-5=0 \\ 3-5=-2 \\ 2-5=-3 \end{gathered}[/tex]Step 3:
Calculate the squares of the mean deviation
[tex](x-\bar{x})^2[/tex][tex]\begin{gathered} 2^2=4 \\ (-4)^2=16 \\ 2^2=4 \\ 5^2=25 \\ 0^2=0 \\ (-2)^2=4 \\ (-3)^2=9 \end{gathered}[/tex]Step 4:
Substitute the values in the formula below
[tex]\begin{gathered} \sigma \left(X\right)=\sqrt{\frac{\sum _{i=1}^n\left(x_i-\bar{x}\right)^2}{n-1}} \\ \sigma\left(X\right)=\sqrt{\frac{4+16+4+25+0+4+9}{7-1}} \\ \sigma\left(X\right)=\sqrt{\frac{62}{6}} \\ \sigma\left(X\right)=3.21 \end{gathered}[/tex]Hence,
The standard deviation of the data to the nearest whole number will be
[tex]3.0[/tex]