Pre-Algebra
Data and graphs
Box and whisker plots
20 practice questions
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Theory + worked examples
Box and Whisker Plots
Texas Pre-Algebra (TEKS) • Standard 6.12(A) • Data & Graphs
Box and Whisker Plots is the opening topic of Data & Graphs in the Texas Essential Knowledge and Skills. It is aligned to Standard 6.12(A), which requires students to construct and interpret box-and-whisker plots.
A box-and-whisker plot displays the five-number summary — minimum, \(Q_1\), median, \(Q_3\), and maximum.
Theory
A box-and-whisker plot shows the five-number summary: minimum, first quartile \(Q_1\), median, third quartile \(Q_3\), and maximum.
The box spans \(Q_1\) to \(Q_3\) (the middle half); the whiskers reach the extremes.
A box-and-whisker plot.
The five-number summary.
Interquartile range:
\[\text{IQR}=Q_3-Q_1\]
The median is the middle value.
How to read a box plot
- Find the five-number summary.
- The box runs \(Q_1\) to \(Q_3\).
- The line in the box is the median.
- Whiskers reach the minimum and maximum.
Example 1 — Median
In the plot, what does the line inside the box show?
Solution
The median.
Example 2 — IQR
With \(Q_1=6\) and \(Q_3=14\), find the IQR.
Solution
Subtract.
| \(14-6\) | \(=\) | \(8\) |
Example 3 — Range
With min \(2\) and max \(18\), find the range.
Solution
Max minus min.
| \(18-2\) | \(=\) | \(16\) |
Example 4 — Middle half
What does the box represent?
Solution
The middle \(50\%\) of the data.
Common pitfalls
The box is the middle 50%, not the whole data.
IQR is \(Q_3-Q_1\), not the range.
The median need not be centered in the box.
Frequently asked questions
What is a box plot?
A display of the five-number summary.
What is the IQR?
\(Q_3-Q_1\).
What does the box show?
The middle 50% of the data.
What is the line inside the box?
The median.
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