What Is a Population?
Let me explain what a population means in statistics. It's the complete pool of data or entities from which you draw a sample for your study. Any group sharing a common feature qualifies as a population, and a sample is just a statistically significant slice of that population.
Key Takeaways
You need to know that a population is the whole group you're gathering and analyzing data on. Collecting data on an entire population is usually tough because of the costs and time involved, so we rely on samples to draw inferences. For the study's results to truly represent the population, your sample has to be randomly selected. Remember, you can pull valid statistics from either a sample or the full population.
Understanding Populations
As a statistician or analyst, you'd ideally want to know every detail about each entity in a population to reach the most accurate conclusions. But that's rarely possible or practical since populations are often huge. That's why you typically take a sample—because measuring every individual is limited by time, resources, and access.
Here's a quick fact: in statistics, 'individual' doesn't always refer to a person; it just means a single entity in the group you're studying.
Take great white sharks in the ocean as an example of a population. You can't realistically gather data on every single one by finding and tagging them all. Instead, marine biologists tag the ones they encounter as a sample and use that to infer details about the whole population. This works because the initial encounters are random, making it a random sampling method.
You can derive valid statistics from a sample or the entire population. The goal with random sampling is to eliminate bias, ensuring every entity in the population has an equal shot at being selected.
How to Measure a Population
Measuring a population depends on what you're analyzing and your goals. You collect data through surveys, measurements, observations, or other methods. But for large populations, gathering all that data isn't feasible due to the high costs, time, and resources needed.
Consider an ad claiming '62% of doctors recommend XYZ for their patients.' They didn't survey every doctor in the U.S.; instead, they sent out surveys to hundreds or thousands and based the claim on the responses. That's a sample of the population.
Population and Investing
A parameter describes a characteristic of a population, while a statistic describes a sample, and you use those to make inferences about the population. Inferential statistics help you make educated guesses about population parameters based on sample data from a random draw.
When statistics like means and standard deviations come from populations, they're called population parameters, often denoted by Greek letters like µ for mean and σ for standard deviation. These are usually inferential because we work with samples, not full populations.
Importantly, if you have all the data for the population, you don't need inferential statistics since you're not sampling.
In market and investment analysis, you use statistics to examine investment data and infer about markets, investments, or indexes. Sometimes, analysts can look at an entire population because price data has been recorded for years. For instance, analyzing every publicly traded stock's price for a market evaluation treats that as a population, and you can calculate parameters directly.
Analysts might use these parameters differently from statisticians or scientists, though.
Parameters in Investing vs. Statistics and Science
- Investment Analysts: Alpha is the excess returns of an asset compared to a benchmark; Standard Deviation is the average variability in prices for measuring volatility and risk; Moving Average smooths short-term price fluctuations to indicate trends; Beta measures an investment's performance against the overall market.
- Statisticians and Scientists: Alpha is the probability of a Type I error, rejecting a true null hypothesis; Standard Deviation is the average variability in data; Moving Average smooths short-term data fluctuations; Beta is the probability of a Type II error, failing to reject a false null hypothesis.
What Is Meant by Population in Statistics?
In statistics, a population is the complete set of events or items you're analyzing, like all the daisies in the U.S.
What Is Population Mean in Statistics?
The population mean is simply the average of all values of interest within that population.
What Statistics Describe a Population?
Statistics describing populations include size, density, distribution, mean, and standard deviation. Usually, analysts and scientists don't have full data on populations, so they use sample statistics to describe them.
The Bottom Line
A population is the statistical pool you're studying and extracting data from. Gathering data on populations can be challenging, especially for broad or dispersed topics. Studying all brown-eyed people worldwide is impossible, so you use random sampling to make inferences. In investment analysis, populations are often specific assets with easily accessible recorded data, unlike data on living organisms which is harder to obtain.
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