We have se following data set expressed in the for (x,P(X=x)):
(7,0.1), (8,0.1), (9,0.3), (10,0.1), (11,0.4)
This is equivalent to a data set (7,8,9,9,9,10,11,11,11,11)
The general formula for the standard deviation of a variable x and a set of n values is given by
[tex]Sd=\sqrt[]{\frac{\Sigma(x_i-\bar{x})^2}{n}}[/tex]
For the given data set, the mean is 9.6 and n = 10
Therefore, we have:
[tex]\begin{gathered} Sd=\sqrt[]{\frac{(7-9.6)^2+(8-9.6)^2+3(9-9.6)^2+(10-9.6)^2+4(11-9.6)^2}{10}} \\ Sd=\sqrt[]{\frac{(-2.6)^2+(-1.6)^2+3(-0.6)^2+0.4^2+4\cdot1.4^2}{10}} \\ Sd=\sqrt[]{\frac{6.76+2.56+3\cdot0.36+0.16+4\cdot1.96_{}}{10}}=\sqrt[]{\frac{18.4}{10}}=1.4\text{ (rounded)} \end{gathered}[/tex]
