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 & Calculation
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.
Frequently Asked Questions
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.