Data Science Normal Data Distribution
The normal distribution is a symmetric, bell-shaped pattern that many real-world measurements follow, and numpy.random.normal generates realistic samples of it in one line.
The Bell Curve
A normal distribution is symmetric around its mean: values close to the average are common, and values get rarer the farther they sit from it in either direction. Plotted as a histogram, it forms the familiar bell shape - tall in the middle, thin at both tails.
Generating Normal Data with NumPy
numpy.random.normal(loc, scale, size) draws size samples from a normal distribution centered at loc (the mean), with scale controlling the standard deviation - how tightly the values cluster around that center.
Example
import numpy as np
import matplotlib.pyplot as plt
# 100,000 samples: mean (loc) = 170, standard deviation (scale) = 10
heights = np.random.normal(170, 10, 100000)
plt.hist(heights, bins=100)
plt.xlabel("Height (cm)")
plt.ylabel("Count")
plt.show()Run this and the histogram comes out symmetric and bell-shaped, peaking around 170 with the bars thinning out evenly toward both 140 and 200. Change scale to 20 and the same bell gets visibly wider and flatter, without moving its center.
Real-World Quantities That Follow It
- Adult height within a population
- Small measurement errors from a precise instrument
- Standardized test scores across a large group of test-takers
- Reaction times averaged across many trials
The 68-95-99.7 Rule
Example
import numpy as np
mean, std = 170, 10
heights = np.random.normal(mean, std, 100000)
within_1_std = (heights > mean - std) & (heights < mean + std)
print("share within 1 std dev:", np.mean(within_1_std)) # close to 0.68
within_2_std = (heights > mean - 2 * std) & (heights < mean + 2 * std)
print("share within 2 std dev:", np.mean(within_2_std)) # close to 0.95
