Standard deviation of a dice roll?

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Discussion Overview

The discussion centers around calculating the standard deviation of a roll from a 50-sided die, specifically seeking methods to do so without directly subtracting the mean from each possible value. The focus includes theoretical approaches and mathematical reasoning.

Discussion Character

  • Mathematical reasoning
  • Technical explanation

Main Points Raised

  • One participant seeks a method to calculate the standard deviation of a 50-sided die without subtracting the mean from each value.
  • Another participant suggests using the averages of the numbers and their squares to find the variance, providing specific formulas for a fair die.
  • A third participant reiterates the formula for variance, emphasizing the relationship between the expected values of the variable and its square.
  • A later reply points out that the formula presented is similar to what was previously stated, indicating a shared understanding of the variance calculation.
  • One participant expresses difficulty in comprehending the verbal explanation of the formula.
  • Another participant finds the explanation of variance straightforward, suggesting differing levels of clarity among participants.

Areas of Agreement / Disagreement

Participants appear to agree on the formulas for calculating variance and standard deviation, but there is a lack of consensus on the clarity of the explanations provided, with some finding them difficult to understand.

Contextual Notes

Participants rely on specific mathematical formulas and definitions, which may depend on the assumptions of a fair die and the interpretation of moments in statistics.

moonman239
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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?
 
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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).
 
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.
 
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.
Your formula is exactly what I posted in words.
 
Yes, but I found the word formula a bit difficult to comprehend.
 
The variance is the second moment minus the square of the first moment.

Looks plain enough to me.
 

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