Sample (Statistics) — Definition, Formula & Examples
A sample is a subset of individuals or observations selected from a larger group (called the population) to represent that group in a statistical study. You collect data from the sample and use it to draw conclusions about the entire population.
A sample is a finite set of observations drawn from a population of size , where , chosen according to a defined selection procedure. Statistics computed from the sample (such as the sample mean ) serve as estimators of the corresponding population parameters (such as the population mean ).
Key Formula
Where:
- = Sample mean, the average of all observations in the sample
- = Sample size (number of observations selected)
- = The value of the i-th observation in the sample
How It Works
Because measuring every member of a population is usually impractical, you select a sample instead. A good sample is representative, meaning its characteristics closely mirror those of the population. Random sampling — where every member has an equal chance of being chosen — is the most common way to achieve this. Once you have your sample data, you calculate statistics like the mean, standard deviation, or quartiles, and use those values to make inferences about the population.
Worked Example
Problem: A school has 800 students. You want to estimate the average number of hours students sleep per night. You randomly select 10 students and record their sleep hours: 7, 8, 6, 9, 7, 8, 7, 6, 8, 7.
Identify the population and sample: The population is all 800 students. The sample is the 10 students you selected.
Compute the sample mean: Add all values and divide by the sample size.
Interpret the result: Based on this sample, you estimate that the average student at the school sleeps about 7.3 hours per night.
Answer: The sample mean is 7.3 hours, which serves as an estimate of the population mean sleep time for all 800 students.
Why It Matters
Nearly every real-world statistic you encounter — polling results, medical study findings, product quality tests — is based on a sample rather than a full population. Understanding samples is essential in AP Statistics, college research methods courses, and any career involving data analysis or scientific research.
Common Mistakes
Mistake: Confusing sample statistics with population parameters.
Correction: The sample mean estimates the population mean , but they are not the same value. Always specify whether a statistic describes a sample or a population, and use the correct notation ( vs. , vs. ).