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Quartiles

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Quartiles

Study Guide

Key Definition

Quartiles divide the data into four equal parts. $Q_1$ is the 25th percentile, $Q_2$ is the median, and $Q_3$ is the 75th percentile.

Important Notes

Quartiles split data into quarters.
$Q_1$ separates the bottom 25% of data.
$Q_3$ separates the top 25% of data.
The interquartile range is $Q_3 - Q_1$.
Quartiles help understand data distribution.
For even-numbered data sets, the median is the average of the two middle values.
This lesson uses the inclusive-median method: include the median when dividing data for quartiles.

Mathematical Notation

$Q_1$ is the first quartile

$Q_2$ is the median or second quartile

$Q_3$ is the third quartile

$+$ represents addition

$-$ represents subtraction

Remember to use proper notation when solving problems

Why It Works

Quartiles provide a clear way to understand data distribution by dividing it into four equal parts using $Q_1$, $Q_2$, and $Q_3$.

Remember

The interquartile range is calculated by $Q_3 - Q_1$, showing the middle 50% of the data.

Quick Reference

Quartile 1:$Q_1$

Median:$Q_2$

Quartile 3:$Q_3$

Interquartile Range:$Q_3 - Q_1$

Understanding Quartiles

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Watch & Learn

Video explanation of this concept

Beginner

Start here! Easy to understand

Beginner Explanation

Quartiles divide data into four equal parts: $Q_1$, $Q_2$, $Q_3$.

Practice Problems

Test your understanding with practice problems

Quick Quiz

Single Choice Quiz

Beginner

What is the first quartile $Q_1$ of the data set: 15, 20, 35, 40, 50?

Real-World Problem

Question Exercise

Intermediate

Teenager Scenario

Emily collected heights of her classmates in inches: 56, 58, 60, 62, 63, 65, 67, 70. Find $Q_1$, $Q_2$, and $Q_3$.

Thinking Challenge

Thinking Exercise

Intermediate

Think About This

Given a data set, how would you calculate the interquartile range $Q_3 - Q_1$?

Challenge Quiz

Single Choice Quiz

Advanced

In a sorted data set, which value is $Q_2$ and why?

Recap

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Review key concepts and takeaways