Mean, Median, Mode, and Range: When to Use Each Statistical Metric

In statistics, we often want to summarize a dataset using a single representative value. This is where measures of central tendency come in: the mean, the median, and the mode. While all three are forms of "averages," they are computed differently and are useful in different contexts.

Definitions and Calculations

• Mean (Arithmetic Average): Sum all numbers in a dataset and divide by the count of numbers. Example for `2, 4, 6`: (2+4+6)/3 = 4.
• Median (Middle Value): Arrange the numbers in ascending order and find the middle number. For an even count, average the two middle values.
• Mode (Most Frequent Value): The number that appears most often in a dataset. A dataset can have one mode, multiple modes, or no mode.

When to Use Each

The Mean is ideal for symmetric numerical data without extreme values. The Median is preferred for skewed data (like household incomes or real estate prices) because it is not affected by extreme outliers. The Mode is most useful for categorical data (e.g. finding the most popular shirt size sold).