What is Variance?
Variance measures the average squared deviation of data values from the mean. It's the foundation of standard deviation and is used throughout statistics and finance to quantify spread.
Variance (σ²) is the average of the squared differences from the mean: σ² = Σ(x−μ)²/n. It's always ≥ 0, and a larger variance means more spread-out data.
- 1↓Find the meanAdd all values and divide by the count.
- 2↓Subtract the meanFind each value's deviation: x − μ.
- 3↓Square each deviationThis removes negative signs: (x−μ)².
- 4Average the squared deviationsDivide the sum by n to get the variance.
Try it: interactive calculator
Step-by-step worked examples
Find the variance of: 2, 4, 4, 4, 5, 5, 7, 9.
Mean = 5 Squared deviations: 9,1,1,1,0,0,4,16 (sum = 32) Variance = 32/8 = 4
Find the variance of: 4, 8, 6, 5, 3.
Mean = (4+8+6+5+3)/5 = 5.2 Squared deviations: 1.44, 7.84, 0.64, 0.04, 4.84 (sum = 14.8) Variance = 14.8/5 = 2.96
A data set has standard deviation 6. What is its variance?
SD = 6 Variance = SD² = 6² = 36
Flashcards
Quick quiz
Q1.What is the variance of 1, 2, 3, 4, 5?
Q2.A data set has standard deviation 3. What is its variance?
Q3.What are the units of variance compared to the original data?
Q4.If all data values are equal, the variance is…
The full card deck, worked steps and AI-tutor support for “What is Variance?” are in Notek — study by hand before your exam.
Common mistakes
Forgetting to square the deviations. — Correct: Deviations must be squared — otherwise positives and negatives cancel to zero.
Confusing variance with standard deviation. — Correct: Variance is in squared units; SD = √variance is in the original units.
Thinking variance can be negative for 'below-average' data. — Correct: Variance is always ≥ 0 because it's built from squared terms.
Always dividing by n−1. — Correct: Divide by n for population variance, n−1 for sample variance — know which one applies.
FAQ
What is variance?
Variance is the average of the squared deviations of data values from the mean.
What is the formula for variance?
σ² = Σ(x−μ)²/n — the average of the squared deviations from the mean.
What are examples of variance?
The data set 2,4,4,4,5,5,7,9 has variance 4; the data set 4,8,6,5,3 has variance 2.96.
How do you calculate variance?
Find the mean, square each value's deviation from the mean, sum those squares, and divide by the number of data points.