Statistic
A statistic is a number that describes some characteristic of a sample. For example, the average test score of 50 randomly chosen students is a statistic — it summarizes part of a larger group, not the whole group.
A statistic is any numerical measure calculated from the observed values in a sample. Because a statistic is based on a subset of a population rather than the entire population, its value typically varies from sample to sample. This variability is known as sampling variability. In contrast, the corresponding value computed from the entire population is called a parameter.
Worked Example
Problem: A teacher randomly selects 8 students from a class of 200 and records their quiz scores: 72, 85, 90, 68, 77, 94, 81, 73. Find the sample mean, and explain why it is a statistic rather than a parameter.
Step 1: Add up all the observed quiz scores.
Step 2: Divide the sum by the number of students in the sample to get the sample mean.
Step 3: Determine whether this value is a statistic or a parameter. The 8 students are a sample drawn from the full class of 200. Because the mean was computed from a sample, not the entire population, it is a statistic. The symbol is used for the sample mean, while would represent the population mean (the parameter).
Answer: The sample mean is . It is a statistic because it was calculated from a sample of 8 students, not the entire class of 200.
Why It Matters
In statistics, you almost never have access to data from an entire population, so you rely on statistics computed from samples to make inferences about population parameters. Understanding the distinction between a statistic and a parameter is essential for interpreting confidence intervals, hypothesis tests, and margin of error — core tools in AP Statistics and in fields like medicine, polling, and quality control.
Common Mistakes
Mistake: Confusing a statistic with a parameter.
Correction: A statistic comes from a sample and is typically denoted with Latin letters (, , ). A parameter describes the entire population and uses Greek letters (, , ). If you only measured part of the group, the result is a statistic.
Mistake: Treating a statistic as a fixed, unchanging number.
Correction: A statistic varies from sample to sample. If you chose a different random sample, you would almost certainly get a different value. This idea — that statistics have their own distribution called a sampling distribution — is fundamental to inference.