What Is Statistics?
Statistics is the science of learning from data when you can't see everything. You almost never get to measure an entire population, so you take a manageable sample, summarize it, and use it to estimate something about the whole, along with how uncertain that estimate is. This course is about doing that well.
Two jobs: describe, then infer
- Descriptive statistics summarizes the data you actually have: averages, spreads, charts. It makes no claims beyond the data in front of you.
- Inferential statistics goes from the sample in hand to a statement about the population you didn't measure. That step brings in uncertainty, and handling uncertainty is most of what the rest of the course teaches.
The vocabulary that trips everyone up
Everything later uses two pairs of words, so get them straight now. If a later term is unfamiliar, the glossary defines every one the site uses.
- A population is everyone/everything you care about; a sample is the subset you actually measure.
- A parameter is a true (usually unknown) number about the population, such as its mean μ (mu). A statistic is the matching number computed from your sample, such as the sample mean x̄. We use the statistic to estimate the parameter.
🎮 Population → Sample → Estimate
The faint cloud is a whole population of 2,000 exam scores; its true mean μ (teal) is the parameter. Take a sample and your sample mean x̄ (orange) is the estimate. Bigger samples tend to give an x̄ closer to μ.
Your estimate is almost never exactly right, but with a bigger sample it's reliably close. To say how close, and how confident you can be, you need sampling distributions, the Central Limit Theorem, and confidence intervals.
Why not just measure everyone?
Usually you can't. The "population" might be all potential customers, every possible repetition of an experiment, or all humans with a condition: too big, too expensive, or not yet existing. A few hundred well-chosen observations can describe a population accurately. They do have to be well chosen. If the sample systematically missed part of the population, analysis afterward cannot put that part back.
Why it matters: every technique ahead follows the same three steps: sample, summarize, generalize. Every later lesson relies on the difference between a parameter and a statistic, and between a population and a sample.
Common questions
What is the difference between a parameter and a statistic?
A parameter is a number that describes the whole population (like the true mean μ), and it's usually unknown. A statistic is the matching number computed from your sample (like x̄), which you use to estimate the parameter. Memory hook: parameter–population, statistic–sample.
What is the difference between descriptive and inferential statistics?
Descriptive statistics summarizes the data you actually collected (means, standard deviations, charts) and claims nothing beyond it. Inferential statistics uses that sample to draw conclusions about the wider population it came from. Because the sample is only part of that population, its conclusions always come with a measure of uncertainty (confidence intervals, p-values).
Do I need to be good at math to do statistics?
Less than most people fear. The arithmetic in an applied course is squaring, adding, dividing and reading a value off a table, and software does all of it for you. The harder part is the reasoning: what a number is evidence for, what could have produced it by chance, and when a conclusion claims more than the data show. People who found algebra a struggle often do well here, and people who found it easy can still fall into the reasoning traps.