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Sistema Matemático Verificado

Normal Distribution Visualizer

Interactive Bell Curve. Visualize Mean, Standard Deviation, and Z-scores.

Última verificación matemática: Ene 2026

From IQ scores to height, nature loves the **Normal Distribution**. Use this tool to visualize the famous "Bell Curve" and understand the Empirical Rule.

✓ Interactive Bell Curve✓ Adjust Mean & Sigma✓ Empirical Rule Calculator✓ Probability Density

Distribution Parameters

0
1

The Bell Curve

Empirical Rule (68-95-99.7)

68% of data falls between:[-1.00, 1.00]
95% of data falls between:[-2.00, 2.00]

This assumes a perfectly normal distribution. Notice how changes in σ (sigma) make the curve wider (flat) or narrower (tall).

¿Qué es 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.

Fórmula

The Probability Density Function (PDF) is given by:

f(x) = 1σ√(2π)e-0.5(x-μσ

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.

Ejemplo de Cálculo

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.

Preguntas Frecuentes

Preguntas comunes sobre esta calculadora

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.