Respuesta :
Sample standard deviation:
[tex]s=\sqrt{\frac{\Sigma(x_i-\bar{x})^2}{n-1}}[/tex]To find the standard deviation of the given set:
1. Fidn the mean:
[tex]\bar{x}=\frac{77+124+77+82+100+139+81}{7}=\frac{680}{7}\approx97.14[/tex]2. Find the (x-mean) for each data:
[tex]\begin{gathered} (77-97.14)=-20.14 \\ (124-97.14)=26.86 \\ (77-97.14)=-20.14 \\ (82-97.14)=-15.14 \\ (100-97.14)=2.86 \\ (139-97.14)=41.86 \\ (81-97.14)=-16.14 \end{gathered}[/tex]3. Square the results you get in previous step:
[tex]\begin{gathered} (-20.14)\placeholder{⬚}^2=405.6196 \\ 26.86^2=721.4596 \\ (-20.14)\placeholder{⬚}^2=405.6196 \\ (-15.14)\placeholder{⬚}^2=229.2196 \\ 2.86^2=8.1796 \\ 41.86^2=1752.2596 \\ (-16.14)\placeholder{⬚}^2=260.4996 \end{gathered}[/tex]4. Add the squares you get in previus step:
[tex]405.6196+721.4596+405.6196+229.2196+8.1796+1752.2596+260.4996=3782.8572[/tex]5. Divide the resull above into n-1:
[tex]\frac{3782.8572}{7-1}=\frac{3782.8572}{6}=630.4762[/tex]6. Find the square root of the quotient you get in previous step:
[tex]s=\sqrt{630.4762}\approx25.109[/tex]