ML Data Distribution

ML Data Distribution: Uniform, Normal, and Skewed Shapes

Data distribution describes how values are spread across their full range—whether they cluster near a bell-shaped center, spread evenly, or lean heavily toward one side. Inspecting distributions early prevents feeding distorted features into linear or distance-based models.

Histograms and summary quantiles reveal distribution shape quickly before you choose scaling or transformation steps.

Normal vs Uniform vs Skewed Distributions

• Uniform Distribution: Every value inside [low, high] has equal probability (like rolling a fair die or random.uniform(0, 10)).
• Normal (Gaussian) Distribution: Most values cluster symmetrically around the mean in a bell curve (random.gauss(mu, sigma)).
• Skewed Distribution: A long tail stretches left or right (common in prices, file sizes, and page views).

import random
import statistics

random.seed(7)
uniform_vals = [round(random.uniform(0, 100), 2) for _ in range(500)]
normal_vals = [round(random.gauss(50, 10), 2) for _ in range(500)]

print("Uniform stdev:", round(statistics.stdev(uniform_vals), 2))
print("Normal  stdev:", round(statistics.stdev(normal_vals), 2))

Handling Heavy Right Skew in ML

When a positive feature like revenue has extreme large values, applying a log transform (math.log1p(x) or np.log1p(x)) compresses the long tail and often improves linear regression accuracy.

Common Mistakes to Avoid

• Assuming real-world metrics are normally distributed: User session lengths, prices, and bug counts are almost always right-skewed.
• Applying math.log(x) when values include 0: log(0) is undefined and raises ValueError; use log1p(x) (log(1 + x)) instead.
• Forgetting to invert target transforms: If you train a regression model to predict log1p(price), apply expm1(pred) before reporting predicted prices.

Frequently Asked Questions

How can I check distribution shape quickly in Python?

Plot a histogram with matplotlib.pyplot.hist(values, bins=30) or compare the mean against the median—when mean >> median, the data is right-skewed.

Do decision trees require normally distributed features?

No. Tree-based models like Random Forests and XGBoost split on rank order, so skewness does not hurt them.

What does random.gauss(mu=50, sigma=10) generate?

It generates floating-point numbers drawn from a normal distribution centered at 50 with a standard deviation of 10.