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Variation of Data

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Variation of Data

Study Guide

Key Definition

The range of a data set is the difference between the highest and lowest values: $\text{range} = \text{highest value} - \text{lowest value}$

Important Notes

The range provides a measure of how spread out the data is.
Quartiles divide data into four equal parts.
The interquartile range measures the spread of the middle 50% of data.
The median is the middle value of the data set.
The range does not account for how data is distributed between extremes.

Mathematical Notation

$-$ represents subtraction

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

$\sqrt{x}$ represents the square root

$x^2$ represents x squared

Remember to use proper notation when solving problems

Why It Works

Understanding variation helps in identifying the dispersion of data, which is crucial for statistical analysis.

Remember

The interquartile range is calculated as $Q_3 - Q_1$.

Quick Reference

Range Formula:$\text{range} = \text{max} - \text{min}$

Interquartile Range:$IQR = Q_3 - Q_1$

Understanding Variation of Data

Choose your learning level

Watch & Learn

Video explanation of this concept

Beginner

Start here! Easy to understand

Beginner Explanation

Simple explanation with $\text{range} = \text{max} - \text{min}$

Practice Problems

Test your understanding with practice problems

Quick Quiz

Single Choice Quiz

Beginner

What is the range of the data set: 5, 8, 12, 15, 21?

Real-World Problem

Question Exercise

Intermediate

Teenager Scenario

You collected the following test scores: 72, 85, 90, 88, 75. Calculate the interquartile range.

Thinking Challenge

Thinking Exercise

Intermediate

Think About This

Find the median and quartiles of the data set: 4, 8, 15, 16, 23, 42, 50.

Challenge Quiz

Single Choice Quiz

Advanced

Given the data set: 17, 23, 23, 38, 45, 56, 59. What is the interquartile range?

Recap

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Review key concepts and takeaways