Statistics
Variance around the expected value
How far the outcomes scatter around the average, weighted by probability.
The Formula
Var = p1 x (x1 - E)^2 + ... + pn x (xn - E)^2
How far the outcomes scatter around the average, weighted by probability.
| Symbol | Meaning | Unit | Notes |
|---|---|---|---|
| Var | Variance | outcome squared | The probability weighted average squared distance. |
| E | Expected value | same as outcome | The centre being measured around. |
| xi | Outcome | same as outcome | Each possible result. |
What Each Symbol Means
Varoutcome squared
Variance
The probability weighted average squared distance.
Esame as outcome
Expected value
The centre being measured around.
xisame as outcome
Outcome
Each possible result.
See It Worked With Real Numbers
A formula on its own does not tell you which number goes where. The how to calculate expected value page applies this equation to a concrete case, shows every intermediate step, and names the mistakes that produce a wrong answer even when the algebra is right.
Where This Formula Appears
This equation is the working core of How To Calculate Expected Value, filed under Math. Every number the guide produces comes from substituting into this one line.