What Are Measures of Central Tendency?
In statistics, a measure of central tendency is a single value that attempts to describe a set of data by identifying the central position within that data set. The three most common measures are the mean, median, and mode.
The Mean (Arithmetic Average)
The mean is computed by summing all data points and dividing by the total number of values.
Example: For dataset [4, 8, 12, 16], Mean = (4 + 8 + 12 + 16) ÷ 4 = 40 ÷ 4 = 10.
Best used for: Symmetric data without extreme outliers (e.g., test scores, height measurements).
The Median (Middle Value)
The median is the exact middle value when a dataset is arranged in ascending order.
Example (Odd Count): For [3, 7, 9, 15, 22], Median = 9.
Example (Even Count): For [2, 5, 8, 12], Median = (5 + 8) ÷ 2 = 6.5.
Best used for: Skewed data with outliers (e.g., household income, home sale prices).
The Mode (Most Frequent Value)
The mode is the value that appears most frequently in a dataset.
Example: For [5, 7, 7, 9, 12], Mode = 7.
Best used for: Categorical or discrete data (e.g., shoe sizes, popular survey choices).
Summary Comparison Table
- Mean: Uses every value, but sensitive to extreme outliers.
- Median: Robust against outliers; ideal for income & housing stats.
- Mode: Useful for identifying peak popularity or categorical trends.