SwadhyAI Notes

All Python notes

Normal Data Distribution 🔔

The Bell Curve

The Normal (or Gaussian) Distribution is the most important probability distribution. It fits many natural phenomena like height, blood pressure, and IQ scores.

✨ Generating Normal Data

Use random.normal(). It takes loc (mean), scale (standard deviation), and size.

python
import numpy as np
import matplotlib.pyplot as plt

# Mean = 5.0, Std Dev = 1.0, Size = 100,000
x = np.random.normal(5.0, 1.0, 100000)

plt.hist(x, 100)
plt.show()

✨ The 68-95-99.7 Rule

In a normal distribution:

  • 68% of data falls within 1 Standard Deviation of the mean.
  • 95% falls within 2 Standard Deviations.
  • 99.7% falls within 3 Standard Deviations.