Data Distributions

The shape of your data – normal, skewed, uniform, bimodal – and why it matters.

Key Points

• Normal (bell) = symmetric, mean = median. Common in nature (heights, errors).
• Right skewed = long tail on the right (income). Mean > median.
• Left skewed = long tail on the left (test scores where most passed). Mean < median.
• Uniform = all values roughly equally common (like dice rolls).
• Bimodal = two peaks, often means two different groups mixed together.
• Always plot before you assume normality.

What it is

A distribution tells you how often each value appears. It's the shape you see when you draw a histogram. Normal looks like a bell. Skewed has a long tail on one side. Uniform is flat. Bimodal has two peaks. The shape decides which summary stats are safe and which models will work.

Why it exists

Different distributions break different assumptions. Many statistical tests assume normality. If your data is skewed, using mean as a summary misleads. If it's bimodal, a single average is meaningless. Knowing the shape protects you from stupid mistakes.

Intuition

When to use

• Before reporting mean vs median – skewed data calls for median.
• Before using t‑tests or linear regression (they assume normality).
• When you see two peaks – consider splitting your data into two groups.

Common mistakes

• Assuming a dataset is normal without checking. Most real data is not.
• Using mean on bimodal data – the average of two peaks is a valley nobody lives in.
• Ignoring skewness when building linear models – they get pulled toward the tail.

In practice

EDA starts with distribution plots. Many ML algorithms perform better with normally distributed features (so people log‑transform skewed data). Clustering algorithms can naturally find the two groups in a bimodal distribution.

Related concepts