These are the three most common ways to find the "center" of a data set:
- Mean: The arithmetic average. Sum all values and divide by count.
- Median: The middle value when data is sorted. Less affected by outliers.
- Mode: The most frequently occurring value. A set can have no mode, one mode, or multiple modes.
Example
Data: 3, 7, 7, 2, 9
- Mean: (3+7+7+2+9) ÷ 5 = 5.6
- Median: Sort → 2, 3, 7, 7, 9 → middle value = 7
- Mode: 7 appears most often = 7
When to Use Each
Use mean for symmetric data. Use median when there are outliers (e.g., income data). Use mode for categorical data (e.g., most popular color).
How Outliers Distort the Mean
A single extreme value can drag the mean far from what "typical" looks like. Ten people earning $50,000 and one earning $5,000,000 have a mean income over $500,000 — wildly misleading — while the median stays at $50,000, accurately reflecting the typical earner. This is exactly why income and home price statistics are almost always reported as medians.
Skewed Distributions
In a symmetric distribution, mean and median are equal. In a right-skewed distribution (like income), the mean is pulled higher than the median by high outliers. In a left-skewed distribution, the mean is pulled lower. Comparing mean to median is a quick way to spot skew in a data set.