STEM Calculators

Standard Deviation of a Discrete Random Variable

Statistics • Discrete Random Variables and Their Probability Distributions

Written by STEM Calculators Team Published Updated
View all topics

Standard Deviation of a Discrete Random Variable

Use a probability distribution (x, P(x)) (or frequencies f(x)) to compute: mean μ, variance Var(X), and standard deviation σ.

μ = Σ x · P(x) and σ = √( Σ x2 · P(x) − μ2 )
Choose an example, then click Fill example (it will NOT auto-fill on reload).
At least 2 rows required.
If ΣP(x) ≠ 1, this divides each P(x) by the total.
Tip: You can type decimals (e.g., 0.30) or fractions (e.g., 3/10).
x P(x)

Rate this calculator

0.0 /5 (0 ratings)
Be the first to rate.
Your rating
You can update your rating any time.

Frequently Asked Questions

What is the mean (expected value) of a discrete random variable?

It is the long-run average outcome you expect if the random process is repeated many times. It is computed from the probability distribution using mu = sum( x * P(x) ).

How do I calculate the mean from a probability distribution table?

Multiply each x value by its probability P(x), then add all the products. The calculator shows this in the x * P(x) column and sums it to get mu.

What makes a discrete probability distribution valid?

Every probability must be between 0 and 1, and the probabilities across all outcomes must add up to 1. A mean is computed from a valid distribution.

Can I use frequencies instead of probabilities to compute the mean?

Yes. When you enter frequencies, the calculator converts them to probabilities by dividing each frequency by the total frequency, then computes the mean from the resulting P(x) values.

Related calculators

Questions related to this topic

Fresh

Most recent questions

2 questions · Sorted by newest first

Showing 1–2 of 2
per page
  1. Jan 31, 2026 Published
    Variance of X − Y (variance x-y) using covariance
    Statistics Discrete Random Variables and Their Probability Distributions Standard Deviation of a Discrete Random Variable
    Open
  2. Jan 23, 2026 Published
    Standard Deviation Sign in Statistics (σ vs s)
    Statistics Discrete Random Variables and Their Probability Distributions Standard Deviation of a Discrete Random Variable
    Open