Standard deviation

• How to Determine Sample Size for a Normal Mean
  Calculate sample size for estimating a normal population mean from the confidence level, desired margin of error, and standard deviation.
• What Are the Expected Value and Standard Deviation of Dice Rolls?
  For a fair six-sided die, the expected roll is 3.5 and the standard deviation is about 1.708; for n independent rolls, use the scaling rules.
• How to Calculate a Z-Score Without a Standard Deviation
  A z-score needs a standard deviation or equivalent information. Learn when it cannot be calculated and how to find or estimate the missing spread.
• What Is the Standard Deviation of an Exponential Distribution?
  For an exponential distribution with rate λ, the standard deviation is 1/λ; with scale θ or mean μ, it equals θ or μ. See the derivation and example.
• Does Standard Deviation Change When You Add or Multiply by a Constant?
  Adding a constant leaves the standard deviation unchanged; multiplying by a scales it by |a| and the variance by a². Proof, examples and the general rule for aX + b.
• Given the Mean and Standard Deviation, How Do You Find a Probability?
  Convert values to z-scores and use the standard normal table to find P(X < b), P(X > a) and P(a < X < b) from a mean and standard deviation, with examples.
• What Is the Standard Deviation of a Dice Roll?
  The standard deviation of one fair six-sided die is √(35/12) ≈ 1.708. See the derivation, the formula for any die, and how it scales for sums and averages.