How to Calculate Variance (Step-by-Step)

Ever heard the term variance in statistics and wondered what it actually means? Don’t worry — it’s not as scary as it sounds!

In this article we provide a variance calculator and explain the concept in a simple way ✨

🙋 What Is Variance?

Variance tells us how spread out the numbers are in a data set. If your numbers are all close to the average (mean), you’ll have a low variance. If the numbers are all over the place, your variance will be higher.

It’s used in statistics, science, finance, sports, and pretty much any field that works with data!

✏️ How to Calculate Variance (Sample)

Let’s use the formula for sample variance, which is most common when you’re working with a portion of a larger population:

s² = Σ(xᵢ - x̄)² / (n - 1)

Where:

• xᵢ = each value in your sample
• x̄ = the sample mean (average)
• n = number of values in the sample
• Σ = sum of all the values

🧮 Step-by-Step Example

Let’s say your data set is:

5, 7, 3, 7, 10

Step 1: Find the Mean

Mean = (5 + 7 + 3 + 7 + 10) / 5 = 32 / 5 = 6.4

Step 2: Subtract the Mean from Each Number (and Square the Result)

Value	xᵢ – x̄	(xᵢ – x̄)²
5	-1.4	1.96
7	0.6	0.36
3	-3.4	11.56
7	0.6	0.36
10	3.6	12.96

Step 3: Add All the Squared Differences

1.96 + 0.36 + 11.56 + 0.36 + 12.96 = 27.2

Step 4: Divide by (n – 1)

Sample Variance = 27.2 / (5 - 1) = 27.2 / 4 = 6.8

🎉 Your sample variance is 6.8

📌 Why Variance Matters

• Helps you understand data variability
• Used in risk analysis and investment decisions
• Supports quality control in manufacturing
• Common in sports stats and scientific research

👀 Quick Tip: Sample vs Population Variance

• Sample Variance divides by (n - 1)
• Population Variance divides by n

Use sample variance when working with a portion of the total data set.

📌 Final Formula Recap (Sample Variance)

s² = Σ(xᵢ - x̄)² / (n - 1)