Parameter (Statistics)
A parameter is a number that summarizes a characteristic of an entire population. For example, the true average height of every student in a country is a parameter.
In statistics, a parameter is a fixed numerical value that describes a measurable characteristic of a population. Parameters are typically unknown because it is rarely possible to measure every member of a population. Instead, statisticians use sample data to estimate parameters through statistics (sample-based values). Common parameters include the population mean , the population standard deviation , and the population proportion .
Worked Example
Problem: A school has exactly 5 students, and their test scores are 72, 85, 90, 68, and 95. Find the population mean and determine whether it is a parameter or a statistic.
Step 1: Identify whether the data covers the entire population. Since the school has exactly 5 students and all 5 scores are given, this is the full population.
Step 2: Calculate the population mean by summing all values and dividing by the population size .
Step 3: Compute the result.
Step 4: Classify the result. Because the mean was calculated using every member of the population, is a parameter, not a statistic.
Answer: The population mean is . Since it describes the entire population, it is a parameter.
Why It Matters
In real life, parameters are almost always unknown. You cannot measure the true average income of every person in a country or the exact proportion of all voters who support a policy. The entire framework of inferential statistics — confidence intervals, hypothesis tests, margin of error — exists because we need to estimate unknown parameters from sample data. Understanding what a parameter is, and how it differs from a statistic, is fundamental to interpreting any statistical study.
Common Mistakes
Mistake: Confusing a parameter with a statistic.
Correction: A parameter describes a population; a statistic describes a sample. Use Greek letters (, , ) for parameters and Roman letters (, , ) for statistics. A helpful mnemonic: population ↔ parameter both start with 'p.'
Mistake: Assuming you can calculate the exact value of a parameter from sample data.
Correction: A value computed from a sample is a statistic — an estimate of the parameter. It will differ from the true parameter due to sampling variability. Only when you have data on every member of the population do you have the actual parameter.