Standard Deviation Calculator

Calculate mean, variance, and standard deviation

📊 Standard Deviation Calculator

Calculate mean, variance, and standard deviation

ℹ️ Sample vs Population

  • • Sample: Part of the data (uses n-1)
  • • Population: All data points (uses n)
  • • Sample SD is typically larger
  • • Use sample when data represents a subset

Statistics

Count (n)
10
Mean (μ / x̄)
5.5000
Standard Deviation (s)
3.0277
Variance (s²)
9.1667
Min
1
Max
10
Range
9
Sum (Σx)
55.0000

📝 Calculation Steps

Step 1: Calculate Mean
μ = Σx / n = 55.00 / 10 = 5.5000
Step 2: Calculate Deviations
(1 - 5.50)² = 20.2500
(2 - 5.50)² = 12.2500
(3 - 5.50)² = 6.2500
(4 - 5.50)² = 2.2500
(5 - 5.50)² = 0.2500
(6 - 5.50)² = 0.2500
(7 - 5.50)² = 2.2500
(8 - 5.50)² = 6.2500
(9 - 5.50)² = 12.2500
(10 - 5.50)² = 20.2500
Step 3: Calculate Variance
s² = Σ(x - μ)² / (n - 1) = 9.1667
Step 4: Calculate Standard Deviation
s = √(variance) = √9.1667 = 3.0277

📐 Sample Formulas

  • • Mean: x̄ = Σx / n
  • • Variance: s² = Σ(x - x̄)² / (n - 1)
  • • Std Dev: s = √s²
  • • Uses n-1 (Bessel's correction)

📏 Population Formulas

  • • Mean: μ = Σx / N
  • • Variance: σ² = Σ(x - μ)² / N
  • • Std Dev: σ = √σ²
  • • Uses N (all data points)

What is Standard Deviation Calculator?

The Standard Deviation Calculator computes mean, variance and standard deviation for a set of numbers. Choose whether the data represents a sample or the entire population.

Enter numbers separated by commas or spaces to get a full set of statistics including count, mean, variance, min, max and range.

Key Features

  1. Sample vs Population – Choose the correct formula (n-1 vs n)
  2. Detailed output – Mean, variance, standard deviation, min, max and range
  3. Calculation steps – See step-by-step formulas and intermediate results
  4. Easy to Use: Simple interface for quick standard deviation calculator operations
  5. Fast Processing: Instant results with high performance
  6. Free Access: No registration required, completely free to use
  7. Responsive Design: Works perfectly on all devices
  8. Privacy Focused: All processing happens in your browser

How to Use

  1. Step 1 – Enter numbers separated by commas or spaces
  2. Step 2 – Select Sample or Population
  3. Step 3 – Review results and calculation steps

Use this tool to understand the spread of your data and make informed decisions based on statistical measures.

Benefits

  • Time Saving: Complete tasks quickly and efficiently
  • User Friendly: Intuitive design for all skill levels
  • Reliable: Consistent and accurate results
  • Accessible: Available anytime, anywhere

FAQ

What is Standard Deviation Calculator?

Standard Deviation Calculator is an online tool that helps users perform standard deviation calculator tasks quickly and efficiently.

Is Standard Deviation Calculator free to use?

Yes, Standard Deviation Calculator is completely free to use with no registration required.

Does it work on mobile devices?

Yes, Standard Deviation Calculator is fully responsive and works on all devices including smartphones and tablets.

Is my data secure?

Yes, all processing happens locally in your browser. Your data never leaves your device.