In order to calculate the variance, use the following formula:
[tex]\sum ^n_{n\mathop=1}(\mu-x_n)^{2}P(x_n)[/tex]
where μ is the mean of the data.
Then, calculate μ:
μ = (1+2+3+4+5)/5 = 3
and replace this value and the values of xn and P(xn) into the formula for the variance, just as follow:
[tex]\begin{gathered} \sigma^2=(3-1)^2(0.06)+(3-2)^{2}(0.14)+(3-3)^{2}(0.43)+ \\ (3-4)^{2}(0.32)+(3-5)^{2}(0.05)=0.9 \end{gathered}[/tex]
Hence, the variance of the given distribution is 0.9
