Descriptive vs. Inferential Statistics

Statistics splits into two broad modes of work:

Descriptive statistics summarize the data you have. Mean, median, standard deviation, a histogram — these describe your sample. They make no claims about a broader population. There's no inference, no probability, no "and therefore." You're just characterizing what's in the table.

Inferential statistics go further. They use your sample to make claims about a population you haven't fully observed. "The new algorithm is significantly better." "Users in segment A convert at a higher rate than users in segment B." These are claims about the world based on limited data — and that's where probability and hypothesis testing enter.

A practical distinction: you'll use descriptive statistics constantly during exploratory data analysis. You'll reach for inferential statistics when you need to make a claim that goes beyond your data — "does this model generalize?", "does this intervention work?", "is this feature actually predictive?"

When I open a new dataset, before any modeling, I run a quick descriptive pass:

• Are my features on wildly different scales? (Scaling will matter.)
• Are any features very skewed? (Transformations may help.)
• Where are the extreme values, and do they make sense?
• What does "typical" look like for each variable?

You'd be amazed how often this five-second check catches data quality problems, label leakage, or misunderstandings about what a column means. Before you train, describe.