Kid-friendly explanation
Imagine a big jar of mixed jelly beans. You cannot taste them all, so you pick a few jelly beans to try. That smaller group you taste is a sample. If you pick them fairly, what you learn from the sample helps you guess what the whole jar is like.
Worked examples
Example 1 (upper elementary):
A school has 400 students. A teacher wants to know how many students like reading mystery books, but does not have time to ask everyone. The teacher randomly chooses 40 students and asks them.
- The 400 students are the population, which is the entire group the teacher cares about.
- The 40 students who are actually asked are the sample.
- If 28 of the 40 students in the sample say they like mystery books, that is 28/40 = 0.7, or 70% of the sample.
- The teacher can use this sample to infer, or make a reasonable guess, that about 70% of all 400 students like mystery books.
Example 2 (middle/high school):
A city has 50,000 households. A researcher wants to estimate the average number of pets per household. It is not practical to visit all 50,000 households, so the researcher uses a random sampling method.
- The researcher randomly selects 500 households from the city list. These 500 households form the sample.
- In the sample, the total number of pets counted is 650.
- The sample mean (average) number of pets per household is 650 / 500 = 1.3 pets.
- Because the sample is random and fairly large compared with the population, the researcher can use this sample mean to estimate that the population mean is about 1.3 pets per household.
- If the researcher took a different random sample of 500 households, the mean might be a little different. That change from sample to sample is called sample-to-sample variability.
Going deeper
In statistics, a sample is the foundation of inferential statistics, which is using data from a sample to learn about a larger population. Because it is often impossible or too expensive to measure everyone, good sampling methods are essential.
A key idea is that a sample should be representative of the population. This usually means using some form of randomization, where every member of the population has a known chance of being chosen. Random samples reduce sampling bias, which happens when some types of people or outcomes are more likely to be included than others.
There are many sampling methods, such as simple random sampling, stratified sampling (splitting the population into groups and sampling from each), cluster sampling (sampling whole groups), systematic sampling (choosing every k-th person), and convenience sampling (choosing whoever is easiest to reach). Only some of these, especially the random ones, usually lead to valid inferences about the population.
Common mistakes
- Mistake: Thinking any small group is a good sample of a population, even if it is chosen for convenience.
Correction: A valid sample should be selected using a method that avoids bias, usually through randomization, so it represents the population fairly. - Mistake: Believing that a bigger sample always removes all uncertainty.
Correction: A larger sample usually reduces the margin of error, but there is always some uncertainty because different random samples can give slightly different results. - Mistake: Confusing the sample with the population, and stating sample results as if they were exact facts about everyone.
Correction: Results from a sample are estimates about the population and should be interpreted as approximations, not exact counts for the whole group.
Everyday connection
Samples show up in everyday life whenever people use surveys or polls. When you hear that "60% of people" prefer a certain snack or that a poll predicts an election result, those numbers come from a sample of people who were asked, not from every single person. Even checking a few fries from a large order to see if they are hot is using a sample to judge the whole batch.