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CalcIntel

Updated · Methodology: named formula library

Standard Deviation Calculator

Calculate mean, variance, and standard deviation for a set of numbers.

Enter numbers separated by commas or spaces.
Mean
6

Mean: 6. Median: 6. Min: 1. Max: 10. Std dev: 3.

Count10
Sum55
Mean6
Median6
Min1
Max10
Std deviation3
Data sources: CalcIntel Formula Library

Why This Calculation Matters

The Standard Deviation Calculator gives you a fast, accurate answer for standard deviation, useful for homework, coursework, or inside a larger problem. The formula is shown below so you can see exactly what the tool is doing and verify it against a textbook or other reference.

How to Use This Calculator

  • Enter your values in the input fields, each one has a label and help text explaining what to type.
  • Results appear instantly as you type; there's no "calculate" button to press.
  • Change any input to compare scenarios side by side.

All math happens in your browser. Nothing you type is sent to a server, saved, or shared.

Standard Deviation

Standard deviation measures how spread out numbers are from the mean (average). A low standard deviation means values cluster near the mean; a high standard deviation means values are more spread out.

Steps

  • Calculate the mean
  • Subtract the mean from each value and square the result
  • Average the squared differences (variance)
  • Take the square root (standard deviation)

Formula

Population SD: σ = √(Σ(x − μ)² / N). Sample SD: s = √(Σ(x − x̄)² / (n − 1)). Sample SD uses n − 1 (Bessel's correction) to correct bias.

Worked Example

Sample dataset: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10

values
1, 2, 3, 4, 5, 6, 7, 8, 9, 10
Result
Mean: 5.5, Median: 5.5, SD: 2.87

Mean = (1+2+...+10)/10 = 5.5. Median = (5+6)/2 = 5.5. Population SD ≈ 2.87.

When to Use This Calculator

  • Check homework, textbook problems, or coursework answers.
  • Explore how the result changes as you vary inputs, great for intuition building.
  • Verify a calculation inside a larger engineering, research, or data workflow.

Limitations & Common Mistakes

  • Results are only as accurate as the inputs, double-check rounding and units.
  • Numeric precision is limited by JavaScript floating-point arithmetic.

Frequently Asked Questions

What does the Standard Deviation Calculator compute?

It computes the mean (average), median, min, max, count, sum, and standard deviation of any list of numbers you enter. Numbers can be separated by commas, spaces, or newlines.

What's the difference between mean and median?

Mean is the arithmetic average (sum / count). Median is the middle value when sorted. Median is more robust to outliers — for income data, real-estate prices, or any skewed distribution, the median is usually the more honest "typical value."

Should I use sample or population standard deviation?

This calculator uses population standard deviation (divides by N). For statistical inference where your data is a sample of a larger population, you'd want sample SD (divides by N−1, Bessel's correction). The difference is small for N > 30.

Can I use this for grades/scores?

Yes — for class grades, test scores, or any list of numerical observations. For weighted averages (e.g., GPA where credit hours matter), use the GPA Calculator instead.

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Key terms

Source: BLS Consumer Price Index, 2026.