# How to Calculate Standard Deviation from Probability & Samples

By Normal we can calculate standard deviation using set of datas (Worksheet for Standard Deviation). We can calculate the Mean and standard deviation using the sample size and probability. using the below formula
Formula for Standard Deviation
sd=√n x p x (1-p)
Formula for Mean
mean= n x p

Example Problem
A Single dice is throw 450 times and find the standard deviation and mean for the probability of getting 5.

From the above problem
No.of Sample N=450
and probability of getting 5 is 1/6

Now appy N and P in above equation to find Standard Deviation and mean,
SD=√n x p x (1-p)
SD=√450 x 1/6 x (1-1/6)
SD=7.9057

Mean = n x p
Mean = 450 x 1/6
Mean = 75

Hence the required Standard Deviation and Mean for the given Probability and samples is
SD=7.9057
mean=75

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