Understanding Averages and Central Tendency
Central tendency refers to the middle or typical value of a data set. There are three main measures of central tendency: mean, median, and mode. Each has its own use cases and advantages.
Mean (Arithmetic Average)
The mean is the sum of all values divided by the number of values. It's the most commonly used measure of average.
Mean = (x₁ + x₂ + ... + xₙ) / n
Best used when: Data is evenly distributed without extreme outliers.
Median
The median is the middle value when data is arranged in order. For an even number of values, it's the average of the two middle values.
Best used when: Data has outliers or is skewed. Median is more robust to extreme values than mean.
Mode
The mode is the value that appears most frequently in a data set. A data set can have one mode (unimodal), multiple modes (multimodal), or no mode (if all values appear equally).
Best used when: Finding the most common value, especially in categorical data.
Range
The range is the difference between the maximum and minimum values. It provides a simple measure of spread or variability.
Range = Maximum − Minimum
When to Use Each Measure
- Mean: Test scores, heights, temperatures (symmetric data)
- Median: Income, house prices, ages (skewed data)
- Mode: Favorite colors, shoe sizes, survey responses (categorical data)