Equations · Probability and statistics
Variance
How spread out values are: the average squared distance from the mean.
σ² = (1/n) ∑ᵢ (xᵢ − μ)²
Aethel says
sigma squared equals the quantity 1 over n, times the sum over i of the quantity x sub i minus mu, squared
What it says
Subtract the mean μ from each value, square the difference so that values above and below count alike, and average the squares. The square root of the variance is the standard deviation σ, in the same units as the data.
This form, dividing by n, is the variance of a whole population. For a sample, books divide by n − 1 instead, which corrects for estimating the mean from the same data.
Symbol by symbol
| Symbol | Say it | Means |
|---|---|---|
| σ² | sigma squared | the variance |
| xᵢ | x sub i | the ith value |
| μ | mu | the mean of the values |
| n | n | how many values there are |
Where you meet it
Every statistics course, quality control and finance.
Questions
How do you say Variance out loud?
σ² = (1/n) ∑ᵢ (xᵢ − μ)² is read: “sigma squared equals the quantity 1 over n, times the sum over i of the quantity x sub i minus mu, squared.” That is exactly what Aethel says when it meets the formula in a book.
What does σ² mean in Variance?
σ² (said “sigma squared”) is the variance.
What does xᵢ mean in Variance?
xᵢ (said “x sub i”) is the ith value.
Can I listen to the equations in my own textbook like this?
Yes. Upload a PDF, EPUB or text file and Aethel reads it aloud with every equation spoken as maths, the way it reads this one, and highlights each sentence as it goes. You can start free.