Mean, Variance, and STDev of a Discrete Random

• The mean of a discrete random variable is also called the expected value of X. It is the weighted average of all the values that the random variable X would assume in the long run.
• Formula for mean (μ):

  μ = 𝐸(𝑋) = ∑[𝑋•𝑃(𝑋)]

  • 𝐸(𝑋) = Expected value of X
  • X = Value of Random Variable
  • 𝑃(𝑋) = Probability of outcome X
• Variance

  • difference between the summation of the products of the squared value of the random variable and its corresponding probability and the square of the mean. It is denoted by sigma squared.
• Formula for Variance:

  σ^2 = ∑[𝑋^2 • 𝑃(𝑋)] − µ^2

  • σ^2 = Variance
  • X = Value of Discrete Random Variable
  • 𝑃(𝑋) = Probability of Discrete Random Variable
  • µ = mean
• Standard Deviation

  • square root of the variance. It is denoted by σ.
• Variance and STDEV

  • measures of dispersion that tells us how spread the scores are from the mean.
  • If the variance is:
  • Small - closer to the mean
  • Large - spread out from the mean
  • Zero - all the scores in the data are equal