Answer:
Explanation:
The mean of the data set is:
[tex]\begin{gathered} \bar{x}=\frac{12+14+1+10+3}{5} \\ \\ =\frac{40}{5}=8 \end{gathered}[/tex]
For x = 12:
[tex]\begin{gathered} x-\bar{x}=12-8=4 \\ (x-\bar{x})^2=4^2=16 \end{gathered}[/tex]
For x = 14:
[tex]\begin{gathered} x-\bar{x}^{}=14-8=6 \\ (x-\bar{x})^2=6^2=36 \end{gathered}[/tex]
For x = 1:
[tex]\begin{gathered} x-\bar{x}^{}=1-8=-7 \\ (x-\bar{x})^2=(-7)^2=49 \end{gathered}[/tex]
For x = 10:
[tex]\begin{gathered} x-\bar{x}^{}=10-8=2 \\ (x-\bar{x})^2=2^2=4 \end{gathered}[/tex]
For x = 3:
[tex]\begin{gathered} x-\bar{x}^{}=3-8^{}=-5 \\ (x-\bar{x})^2=(-5)^2=25 \end{gathered}[/tex]
Sum is: S = 16 + 36 + 49 + 4 + 25 = 130
Standard Deviation:
[tex]\begin{gathered} SD=\sqrt[]{\frac{S}{5}}=\sqrt[]{\frac{130}{5}} \\ \\ =\sqrt[]{26}=5.1 \end{gathered}[/tex]
