Respuesta :
The standard derivation of the sample (s) is:
[tex]s=\sqrt{\frac{\sum_{i\mathop{=}1}^n(x_i-x)^2}{(n-1)}}[/tex]Where:
s = standard derivation of sample
n = number of data provided
xi = each of the values of the sample
x = the mean of xi
So, first, let's find the mean.
Given:
n = 6
The mean is:
[tex]\begin{gathered} x=\frac{\sum_{i\mathop{=}1}^nx_i}{n} \\ x=\frac{13+7+34+25+14+27}{6} \\ x=\frac{120}{6} \\ x=20 \end{gathered}[/tex]And the standard derivation:
[tex]\begin{gathered} s=\sqrt{\frac{(13-20)^2+(7-20)^2+(34-20)^2+(25-20)^2+(14-20)^2+(27-20)^2}{6-1}} \\ s=\sqrt{\frac{(-7)^2+(-13)^2+(14)^2+(5)^2+(6)^2+(7)^2}{5}} \\ s=\sqrt{\frac{524}{5}} \\ s=10.24 \end{gathered}[/tex]Answer: 10.24.
