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Mean, Median, and Mode

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Mean, Median, and Mode

Study Guide

Key Definition

Mean: The sum of all numbers divided by the count of numbers: $\frac{\sum \text{numbers}}{n}$. Median: The middle value in an ordered data set (or the average of two middle values if the set has an even number of items). Mode: The most frequently occurring value in a data set.

Important Notes

Mean is also called the average.
Median is the middle value when data are sorted.
Mode is the value that appears most often.
The formula for mean: $\frac{\text{sum of numbers}}{n}$.
Mean is sensitive to outliers; median is robust against outliers.
Mode can be used with nominal data.
Different measures of central tendency serve different purposes.

Mathematical Notation

$\sum$ represents summation

$\frac{a}{b}$ represents division

Remember to use proper notation when solving problems

Why It Works

Different measures give different perspectives: the mean averages all data, the median locates the center without extreme influence, and the mode identifies the most common value.

Remember

Mean: add all numbers and divide by the count. Median: order values and find the middle. Mode: find the most frequent value.

Quick Reference

Mean Formula:$\frac{\sum{\text{numbers}}}{n}$

Median Definition:Middle value of ordered dataset

Mode Definition:Most frequently occurring value

Understanding Mean, Median, and Mode

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Video explanation of this concept

Beginner

Start here! Easy to understand

Beginner Explanation

Mean is the sum of all numbers divided by how many there are. Median is the middle value when you sort the numbers. Mode is the number that appears most often.

Practice Problems

Test your understanding with practice problems

Quick Quiz

Single Choice Quiz

Beginner

What is the mean of the set {2, 5, 5, 6, 8, 8, 9, 11}?

Real-World Problem

Question Exercise

Intermediate

Teenager Scenario

You scored 85, 90, and 88 on your math tests. What is your average score?

Thinking Challenge

Thinking Exercise

Intermediate

Think About This

A group of friends has pocket money of $5, $10, $15, $20, and $25. What is the mean amount of pocket money?

Challenge Quiz

Single Choice Quiz

Advanced

The following numbers represent daily sales (in dollars): {150, 200, 250, 300, 350, 400, 500}. What is the mean daily sales?

Recap

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Review key concepts and takeaways