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Box-and-Whisker Plots

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Box-and-Whisker Plots

Study Guide

Key Definition

A Box-and-Whisker plot is a graphical representation of a data set that includes the median, upper quartile (Q3), lower quartile (Q1), and the minimum and maximum data values.

Important Notes

The box in a box-and-whisker plot represents the interquartile range.
The whiskers represent the remaining data distribution outside the interquartile range.
The median is represented by a line in the box.

Mathematical Notation

$Q_1$: Lower Quartile

$Q_2$: Median

$Q_3$: Upper Quartile

Remember to use the correct quartile notation when interpreting box-and-whisker plots.

Why It Works

Box-and-whisker plots work by providing a visual summary of a data set's distribution. The box represents the interquartile range, where 50% of the data lies. The whiskers extend to the most extreme data values within 1.5 × IQR of the first and third quartiles. Data points beyond this range are plotted individually as outliers. This gives a quick visual interpretation of the data's dispersion and skewness.

Remember

Remember that outliers, if any, are represented by individual points or asterisks outside the whiskers.

Quick Reference

Median:$Q_2$

Lower Quartile:$Q_1$

Upper Quartile:$Q_3$

Understanding Box-and-Whisker Plots

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Video explanation of this concept

Beginner

Start here! Easy to understand

Beginner Explanation

Box-and-whisker plots are a way to visually summarize the distribution of a data set. The 'box' represents the middle 50% of the data, and the 'whiskers' represent the rest of the data.

Practice Problems

Test your understanding with practice problems

Quick Quiz

Single Choice Quiz

Beginner

What does the box in a box-and-whisker plot represent?

Real-World Problem

Question Exercise

Intermediate

Exam Scores

A data set of students' exam scores has the following five-number summary: • Minimum = 60 • Q1 = 70 • Median = 80 • Q3 = 90 • Maximum = 100 What does this tell you about the distribution of scores?

Thinking Challenge

Thinking Exercise

Intermediate

Think About This

What information can you obtain from a box-and-whisker plot?

Challenge Quiz

Single Choice Quiz

Advanced

If the box in a box-and-whisker plot is skewed to the right, what does this indicate about the data?

Recap

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Review key concepts and takeaways