Mean vs Median

Understanding the differences between these two measures of central tendency and their behavior in different data distributions

Mean

Median

Basic Concepts

Mean

The mean is the sum of all data points divided by the number of data points. It is sensitive to all values, including outliers.

Formula: Mean = (x₁ + x₂ + ... + xₙ) / n

Median

The median is the middle value in a sorted list of numbers. It is not sensitive to outliers and better represents the central value.

Formula: For odd n, Median = x₍ₙ₊₁₎/₂; For even n, Median = (xₙ/₂ + xₙ/₂₊₁) / 2

Interactive Demo

Mean

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Median

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Adjust Data Points

Drag the sliders to change values and observe how mean and median respond

Key Differences

Sensitivity to Outliers

Mean is heavily influenced by outliers, while median remains relatively stable.

Data Distribution

In symmetric distributions, mean and median are close; in skewed distributions, they differ significantly.

Use Cases

Mean works well for symmetric distributions without outliers; median is better for skewed data with outliers.

Practice Questions

Question 1

For the dataset: 3, 5, 7, 9, 100. Which measure better represents the central tendency?

Mean Median

Question 2

In a symmetrically distributed dataset, what is the relationship between mean and median?

Mean equals median Mean is greater than median Mean is less than median

Summary

When to Use Mean?

When data is relatively symmetrically distributed
When there are no extreme outliers
When you need to consider the impact of all data points
When data follows a normal distribution

When to Use Median?

When data is skewed
When there are extreme outliers
When you need a robust measure of central tendency
When dealing with ordinal data

Understanding the difference between mean and median is fundamental to data analysis. Choosing the appropriate measure of central tendency leads to more accurate data interpretation.