Normal Distribution
Calculate probability density for normal distribution
Interactive Sandbox
Adjust values in real-time and observe mathematical cause-and-effect
Central Tendency & Dispersion: Measures the central average (mean) and spread of variability (standard deviation).
Variable Mechanics
Roles, constraints & impacts
Value
Formula Parameter
Mean
Formula Parameter
Standard deviation
Formula Parameter
At a Glance
Gotchas, units & real-world use
Formula Nature & Mechanics
Central Tendency & Dispersion: Measures the central average (mean) and spread of variability (standard deviation).
Common Mistakes & Traps
- Confusing Population Standard Deviation (divide by N) with Sample Standard Deviation (divide by n - 1 for Bessel correction).
- Assuming all distributions are normal (skewed distributions make the median more reliable than mean).
- Outliers disproportionately distort the mean and variance.
Dimensional Analysis & Units
Mean & SD share the same unit as original data; Variance is in [Unit]².
Real-World & Industry Application
Quality control tolerances in manufacturing, stock market volatility metrics, clinical medical trials, and academic grading curves.
Worked Example: Normal Distribution
Given:
- x = 0
- μ = 0
- σ = 1
- f(0) = (1/1√(2π)) × e^(-½((0-0)/1)²)
- = (1/√(2π)) × e^0
- = 1/√(2π) = 0.399
Answer: 0.399
Frequently Asked Questions
What is the Normal Distribution formula?
f(x) = (1/σ√(2π)) × e^(-½((x-μ)/σ)²). Calculate probability density for normal distribution.
How do I calculate Normal Distribution?
Enter Value (x), Mean (μ), Standard deviation (σ) into the calculator. It applies f(x) = (1/σ√(2π)) × e^(-½((x-μ)/σ)²) and shows every step of the working.
Related Statistics Calculators
Partner Spotlight
