Variance
Average squared deviation from the mean.
Key idea
Average squared deviation from the mean.
In depth
Variance is the average squared distance from the mean: σ² = Σ(x − μ)²/n. Squaring removes signs and emphasises large deviations. Its units are the squares of the data units.
Worked example
Data 2, 4, 6: mean 4, deviations −2, 0, 2, squares 4, 0, 4, variance 8/3 ≈ 2.67.
Formula
Real-world uses
- Measuring how consistent a manufacturing process is
- Comparing the risk of two investments
Common mistake
Forgetting that variance has squared units, so it is not directly comparable to the data.
How to learn this
- Read the key idea and say it in your own words.
- Work through the worked example, then try a similar problem.
- Use the interactive lesson’s visual and mini-quiz to check the pattern.
Frequently asked questions
What is Variance?
Average squared deviation from the mean. It is a topic at the advanced level in Probability & Statistics.
What is the formula for Variance?
The key formula is σ² = Σ(x−μ)²/n.
Where is Variance used in real life?
Real-world examples: Measuring how consistent a manufacturing process is; Comparing the risk of two investments.
What should I learn before Variance?
Make sure you are comfortable with Outliers, the previous topic in Probability & Statistics.
What is a common mistake with Variance?
Forgetting that variance has squared units, so it is not directly comparable to the data.
How can I practise Variance?
Open the interactive lesson, play with the visual, then answer the three-question mini-quiz. Getting two right marks the topic complete.
What comes after Variance?
Move on to Standard Deviation next.
Related advanced topics in Probability & Statistics
- Quartiles and IQR – Quartiles split data into four parts; IQR = Q3 − Q1.
- Box Plots – Five-number summary visualised.
- Outliers – Values beyond 1.5 IQR from the quartiles.
- Standard Deviation – Square root of variance; typical spread.
- Sample vs Population Variance – Divide by n−1 for sample variance.
- Weighted Mean – Average where values have different importance.