Your formula is exactly what I posted in words.dalcde said:An alternative formula for the variance (the square of the s.d.) is [tex]\mbox{var}(X)=E[X^2]-E[X]^2[/tex]. The derivation can be found on wikipedia. Use the formulas provided by mathman above to find the value.
The variance is the second moment minus the square of the first moment.
The standard deviation of a dice roll is a measure of how spread out the possible outcomes are from the average roll. It tells us how much the rolls vary from each other.
The standard deviation of a dice roll can be calculated by taking the square root of the average of squared differences between each roll and the mean roll. This is also known as the root mean square deviation.
A higher standard deviation in a dice roll indicates that there is more variability in the possible outcomes. This means that the rolls are more spread out and less likely to be close to the average roll.
No, the standard deviation of a dice roll cannot be negative. It is always a positive value as it is a measure of distance from the mean.
The number of dice rolled does not affect the standard deviation itself, but it does affect the range of possible outcomes. The more dice that are rolled, the smaller the range of possible outcomes and the lower the standard deviation will be.