Mean

TL;DR

A single-value measure of central tendency computed by summing values and dividing by their count.
Useful for summarizing a data set but sensitive to extreme values or outliers.
Most appropriate when the data are evenly distributed or approximately symmetric.

Definition

Mean is a term used in statistics to describe the central tendency of a set of data. It is also known as the average and is calculated by adding up all the values in a data set and dividing by the number of values in the set.

Explanation

The mean provides one value that represents the typical or average observation in a data set. It summarizes and simplifies the data, making it easier to understand and interpret. Because the mean incorporates every value in the data set, individual extreme values (outliers) can substantially affect it. When data are skewed or have long tails, the mean may not accurately reflect the central tendency, and other measures such as the median or mode may be more suitable.

Examples

Class test scores

A teacher with a class of 30 students calculates the average test score by adding all the test scores and dividing the sum by 30. The resulting mean score is used to evaluate the class’s overall performance and identify areas for improvement.

Survey of incomes

Researchers conducting a survey to determine the average income of a population collect income data from a sample of individuals and calculate the mean income by summing all income values and dividing by the number of individuals in the sample. The mean income can then be used to represent the average income of the population and to compare with other populations or time periods.

Use cases

Evaluating overall group performance (for example, a class average).
Representing the average value of a sampled population (for example, average income) for comparison across populations or time periods.

Notes or pitfalls

The mean is sensitive to extreme values or outliers; a very high or very low value can significantly impact the mean.
The mean is most appropriate when the data are distributed evenly or symmetrically; for skewed data, the median may better represent central tendency.

Median
Mode