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गणितीय प्रणाली सत्यापित

Normal Distribution Visualizer

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

अंतिम गणितीय सत्यापन: जनवरी 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).

Normal Distribution Visualizer क्या है?

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.

सूत्र

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.

उदाहरण गणना

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.

अक्सर पूछे जाने वाले प्रश्न

इस कैलकुलेटर के बारे में सामान्य प्रश्न

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.