Statistics is the science of collecting, summarizing, and drawing conclusions from data. It splits into two halves: descriptive statistics (summarizing what you have) and inferential statistics (using a sample to make claims about a larger population).
Center — the “typical” value
| Measure | Meaning |
|---|---|
| Mean | The average (sum ÷ count) |
| Median | The middle value when sorted |
| Mode | The most frequent value |
The median is often more representative than the mean when data has outliers (a few very large or small values).
Spread, and sampling
Range is max minus min; standard deviation measures how far values typically fall from the mean. Two datasets can share a mean but differ wildly in spread, which is why center alone isn’t enough. Because we usually can’t measure everyone, we take a sample and use inferential tools to estimate the whole population — always with some quantified uncertainty.
Frequently asked questions
Mean vs median? Mean is the average; median is the middle value, which resists outliers.
What is standard deviation? A measure of how spread out values are around the mean.
Descriptive vs inferential statistics? Describing your data vs drawing conclusions about a larger group.
A good first habit is to always look at your data, not just its summary numbers. A simple plot reveals outliers, skew, and patterns that a mean or median can hide entirely — two datasets with identical averages can tell completely different stories.