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Mean, Median, Mode

Overview

Finding the 'Average'.

What is it?

Measures that identify the central point of a dataset: Mean (Arithmetic Average), Median (Middle Value), Mode (Most Frequent).

History

The concept of 'Average' was popularized by Adolphe Quetelet to define the 'Average Man' (l'homme moyen) in sociology.

Key Idea

Mean is Mean (math work). Median is the Median Strip (middle of road). Mode is Most (popular).

Practice This Topic

Concept Guide

Plain English: Data is messy. We need one number to represent the whole pile. Mean is the fair share. Median is the exact midpoint (good for ignoring billionaires in wealth stats). Mode is just a popularity contest.

Real-world example: Real Estate. Home prices are always listed as 'Median Price' because one mega-mansion would skew the 'Mean' way too high.

How to do it

  1. Mean: Add all numbers, divide by the count.
  2. Median: Sort numbers from small to big. Pick the middle one. (If 2 in middle, average them).
  3. Mode: Count how many times each number appears. Pick the winner.
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Common Pitfall

Thinking Mean and Median are the same. In skewed data (like income), they are very different.

Word Problem
"A student scores 0, 100, 100 on three quizzes. Which measure makes them look best?"
Reasoning: Mean is (200/3) = 66. Median is 100 (0, 100, 100). Mode is 100. Median and Mode make them look like an A student.

Practice Examples

Data Set
[2, 5, 5, 9]
Mean=5.25, Median=5, Mode=5