Normal Distribution Visualizer
Interactive Bell Curve. Visualize Mean, Standard Deviation, and Z-scores.
From IQ scores to height, nature loves the **Normal Distribution**. Use this tool to visualize the famous "Bell Curve" and understand the Empirical Rule.
Distribution Parameters
The Bell Curve
Empirical Rule (68-95-99.7)
This assumes a perfectly normal distribution. Notice how changes in σ (sigma) make the curve wider (flat) or narrower (tall).
What is Normal Distribution Visualizer?
What is Normal Distribution?
Also known as the Gaussian distribution, it describes a symmetric plot of data where most values cluster around the central "mean", and taper off symmetrically towards the extremes.
Ideally, the Mean, Median, and Mode are all the same.
Formula
The Probability Density Function (PDF) is given by:
Key Parameters
- μ (Mu): The Mean or center of the curve. Shifts it left/right.
- σ (Sigma): The Standard Deviation. Controls the width/spread. Small σ = Tall/Skinny. Large σ = Short/Fat.
Example Calculation
IQ Scores
IQ is designed to be normally distributed with:
- Mean (μ) = 100
- Standard Deviation (σ) = 15
Set these values above. You'll see that ~68% of people have an IQ between 85 and 115.
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Frequently Asked Questions
Common questions about this calculator
Why 68-95-99.7?
It's a mathematical property of the integral of the Gaussian function. 68.2% of the area is within 1 standard deviation, 95.4% within 2, and 99.7% within 3.