SOLUTION
We want to find the standard deviation of the data in the picture
So we need to make a table
The formula is given as
[tex]\sqrt[]{\sum^{}_{}(x-\operatorname{mean})^2.P(x)}[/tex]
So we need to make a table for
[tex]\begin{gathered} x-\operatorname{mean} \\ \text{This is given as } \\ (x-x(Px) \end{gathered}[/tex]
Then we square it and multiply for by P(x)
This means we need a table for
[tex](x-\operatorname{mean})^2.P(x)[/tex]
Then we sum and get the square root.
The table is shown below
So the last column is
[tex]\begin{gathered} (x-xP(x))^2.P(x) \\ It\text{ is the same as } \\ (x-\operatorname{mean})^2.P(x) \end{gathered}[/tex]
So let us sum
[tex]\begin{gathered} (x-xP(x))^2.P(x) \\ We\text{ will add the numbers under it. This is } \\ =2.113819605 \end{gathered}[/tex]
The standard deviation becomes
[tex]\begin{gathered} S\mathrm{}D=\sqrt[]{2.113819605} \\ S\mathrm{}D=1.453898 \end{gathered}[/tex]
Hence the answer is 1.45 to 2 decimal places
