IntroStatsCalc

Discrete Probability Distribution

Mean (expected value), variance, and standard deviation of a probability table.

Inputs

Paste or type numbers separated by commas, spaces, or new lines. A column copied from Excel or Google Sheets works too.

Same order as the values. They must add up to 1.

Results update as you type.

Results

μ = 1.95  ·  σ = 1.1169

In the long run, X averages 1.95 per trial, and a typical outcome is about 1.1169 away from that.

Probability histogram: P(0) = 0.1, P(1) = 0.25, P(2) = 0.35, P(3) = 0.2, P(4) = 0.1.01234x

Results

Σ P(x)1
Mean μ = E(X)1.95
Variance σ²1.2475
Standard deviation σ1.1169
Work table
xP(x)x · P(x)(x − μ)² · P(x)
00.100.3803
10.250.250.2256
20.350.70.0009
30.20.60.2205
40.10.40.4203
Sum11.951.2475

On the TI-84

Put x in L1 and P(x) in L2. STAT → CALC → 1:1-Var Stats, List: L1, FreqList: L2. Then x̄ is μ and σx is σ.

1-Var Stats L1, L2

Show steps
  1. Check. Every P(x) is between 0 and 1 and they add to 1.
  2. Mean. μ = Σ x · P(x) = 1.95
  3. Variance. σ² = Σ (x − μ)² · P(x) = 1.2475
  4. Standard deviation. σ = √1.2475 = 1.1169

About this calculator

Valid distributions

A table of values and probabilities is a probability distribution only if every probability is between 0 and 1 and they all add up to exactly 1.

Expected value

The mean μ, also called the expected value E(X), is the long-run average if you repeated the experiment many times. It doesn't have to be one of the possible values; a family can't have 1.8 children, but the average can be 1.8. The standard deviation σ measures how much the outcomes typically vary from μ.

More probability calculators: Counting (nPr, nCr) · Binomial · Poisson · Geometric