The standard deviation is [tex]\sigma=1.676[/tex]
Step-by-step explanation:
The given data are [tex]1,1,2,2,2,2,3,3,4,7[/tex]
Thus, [tex]N=10[/tex]
The mean for the data is given by
[tex]\begin{aligned}\mu &=\frac{\text {Sum of data}}{N} \\&=\frac{1+1+2+2+2+2+3+3+4+7}{10} \\&=\frac{27}{10} \\\mu &=2.7\end{aligned}[/tex]
The standard deviation is given by
[tex]\sigma=\sqrt{\frac{1}{N} \sum_{i=1}^{N}\left(x_{i}-\mu\right)^{2}}[/tex]
Substituting the values in the formula and simplifying the equation,we get,
[tex]$=\sqrt{\frac{1}{10}(2.89+2.89+0.49+0.49+0.49+0.49+0.09+0.09+1.69+1.69+18.49)}$=\sqrt{\frac{1}{10}(28.1)}$=\sqrt{2.81}$=1.676$[/tex]Thus, the standard deviation for the data is [tex]\sigma=1.676[/tex]
