What you will learn
- Define data and an observation
- Tell the difference between a population and a sample
- Explain why we usually work with samples instead of whole populations
- Tell the difference between a parameter and a statistic
Before we can measure anything, we need to be clear about what we are measuring. Statistics always starts with data, and with a simple question: are we looking at everything, or just a piece of it? Getting this straight now will save you confusion later, because almost every statistic you compute is really an educated guess about a larger group you cannot fully see.
Identifying a sample and population (Khan Academy)
A crisp, beginner walkthrough of the difference between a population and a sample, with clear examples. Watch this first.
Data and observations
Data is simply a collection of recorded facts or measurements. Each individual measurement is called an observation. If you write down the height of every student in a class, each height is an observation, and the whole list is your data. In finance, a single day's return on a stock is an observation, and a year of daily returns is a dataset. Data is the raw material of everything in this unit.
Population versus sample
A population is the entire group you actually care about. A sample is a smaller subset of that population that you actually measure. Suppose you want to know the average height of every adult in a country. The population is every adult in the country. Measuring all of them is impossible, so instead you measure a sample, maybe a few thousand people, and use it to estimate the answer for the whole population.
Key terms
- Data
- A collection of recorded facts or measurements.
- Observation
- A single recorded measurement, like one student's height or one day's return.
- Population
- The entire group you care about, such as every adult in a country.
- Sample
- A smaller subset of the population that you actually measure.
| Population | Sample | |
|---|---|---|
| What it is | The whole group of interest | A subset you actually measure |
| Size | Often huge or infinite | Manageable |
| Everyday example | Every adult in a country | A few thousand surveyed adults |
| Finance example | Every daily return a stock will ever have | The last few years of daily returns |
Why we work with samples
In the real world you almost never have the whole population. Measuring everyone is too expensive, too slow, or simply impossible. In finance the problem is even deeper. The population of a stock's returns is not just its past returns but every return it could ever produce, including the future, which you can never observe. So you are always working with a sample, a limited window of history, and trying to reason about a much larger, partly unknowable population. It's worth keeping that in mind. Your data is a peek through a keyhole, not the whole room.
Population or sample?
A researcher wants to understand how the entire US stock market behaves. She collects the daily returns of the 500 stocks in the S&P 500 over the past 10 years. In this study, the 10 years of returns she collected is best described as...
The 10 years of returns is a sample. The population, the market's behavior across all time including the unobservable future, is far larger. Almost all financial data is a sample of a bigger, partly unknowable population.Parameter versus statistic
This pair of words trips up many beginners, so learn it now. A parameter is a number that describes the whole population, like the true average height of every adult in a country. A statistic is a number computed from your sample, like the average height of the few thousand people you measured. You almost never know the parameter directly. Instead you compute a statistic from your sample and use it as your best estimate of the parameter. Much of statistics is using a sample statistic to guess a population parameter, and knowing how much to trust that guess.
A parameter is the truth about the whole population. A statistic is your best guess at it, computed from the sample you actually have.
Population and estimated parameters, clearly explained (StatQuest)
Josh Starmer explains why we sample and estimate population parameters, with StatQuest's clear intuition. This idea underpins the whole unit.
Match the term
Pair each statistics term with what it means.
Why the distinction matters
Explain in a sentence or two why it is important to remember that a statistic from a sample is only an estimate of the true population parameter, especially in finance.
Write an answer before comparing it with the model response.
Model answer
A sample is only a slice of the population, so any statistic I compute from it, like an average return or a volatility, is just an estimate and could differ from the true value. In finance this matters a lot because my data is always a limited window of history, and the future part of the population is unobservable. Treating a sample statistic as if it were the exact truth leads to overconfidence, so I should hold my estimates with appropriate caution.
You now know that we reason from samples to populations. Next we look at the different kinds of data those samples can contain, because the type of variable decides which statistics even make sense.