First you need to calculate the (estimated) mean, which is:

mean = sum (P(x) * x) for all x. Here we have:

mean = 23*0.05 + 34*0.44 + 45*0.19 + 56*0.11 + 67*0.21

= 44.89

Now we can find the variance, which is the sum of squares of the distance to the mean:

variance = 0.05*(23-44.89)^2 + 0.44*(34-44.89)^2 + 0.19*(45-44.89)^2 + 0.11*(56-44.89)^2 + 0.21*(67-44.89)^2

= 192.3779

So the standard deviation is sqrt(variance) = 13.87

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