Sample vs Population Variance
Divide by n−1 for sample variance.
Key idea
Divide by n−1 for sample variance.
In depth
For a sample, divide by n − 1 instead of n: s² = Σ(x − x̄)²/(n − 1). A sample’s deviations from its own mean are slightly too small, and the n − 1 correction (Bessel’s correction) makes the estimate unbiased.
Worked example
Data 2, 4, 6: sample variance = 8/2 = 4, SD = 2.
Formula
Real-world uses
- Choosing the correct formula when estimating spread from a sample of customers
Common mistake
Using n − 1 when you have the entire population.
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 Sample vs Population Variance?
Divide by n−1 for sample variance. It is a topic at the advanced level in Probability & Statistics.
What is the formula for Sample vs Population Variance?
The key formula is s² = Σ(x−x̄)²/(n−1).
Where is Sample vs Population Variance used in real life?
Real-world examples: Choosing the correct formula when estimating spread from a sample of customers.
What should I learn before Sample vs Population Variance?
Make sure you are comfortable with Standard Deviation, the previous topic in Probability & Statistics.
What is a common mistake with Sample vs Population Variance?
Using n − 1 when you have the entire population.
How can I practise Sample vs Population 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 Sample vs Population Variance?
Move on to Weighted Mean 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.
- Variance – Average squared deviation from the mean.
- Standard Deviation – Square root of variance; typical spread.
- Weighted Mean – Average where values have different importance.