# Difference between parameter and statistic

The difference between parameter and statistic is simple as you shall see in this lesson.

The mean, median, mode, range, variance, or standard deviation, or any other numerical measure is called a parameter when the data set represent the entire population.

The mean, median, mode, range, variance, or standard deviation, or any other numerical measure is called a statistic when the data set is a sample of the population.

For example, after 5000 students took a state test, the raw data is given to you to find the mean and standard deviation.

If you use a sample of 100 students to find the mean and the standard deviation, the mean or standard deviation is called a sample statistic or simply a statistic.

If you use the entire population of 5000 students to find the mean and the standard deviation, the mean or the standard deviation is called a population parameter or simply a parameter.

Take a look at the following formulas that we derived in the lesson about standard deviation.

$$σ = \sqrt {\frac{Σ(x - µ)^{2}} {N} }$$
$$s = \sqrt {\frac{Σ(x - \bar x)^{2}} {n - 1} }$$
µ  and σ are called population parameters

s and x are called sample statistics

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