Standard deviation of a dice roll?

[moonman239]

Let's say I have a big, 50-sided die, with values ranging from 1-50. I want to find the exact standard deviation of the dice roll by hand. I would like to avoid subtracting the mean from each possible value, if at all possible.

How do I do that?

 

[mathman]

The most direct way is to get the averages of the numbers (first moment) and of the squares (second moment). The variance is the second moment minus the square of the first moment. The moments are (n+1)/2 and (n+1)(2n+1)/6 assuming a fair die. (Your n=50).

 

[dalcde]

An alternative formula for the variance (the square of the s.d.) is $$\mbox{var}(X)=E[X^2]-E[X]^2$$. The derivation can be found on wikipedia. Use the formulas provided by mathman above to find the value.

 

[mathman]

An alternative formula for the variance (the square of the s.d.) is $$\mbox{var}(X)=E[X^2]-E[X]^2$$. The derivation can be found on wikipedia. Use the formulas provided by mathman above to find the value.

Your formula is exactly what I posted in words.

 

[dalcde]

Yes, but I found the word formula a bit difficult to comprehend.

 

[mathman]

The variance is the second moment minus the square of the first moment.

Looks plain enough to me.