Reading and Interpreting Box Plots Cheat Sheet

Box plots show how a data set is spread out using five important values: the minimum, first quartile, median, third quartile, and maximum. This cheat sheet helps students read the parts of a box plot, connect each part to the data, and describe center and spread clearly. Students in grades 7 to 9 need these skills to compare groups, identify unusual values, and explain what a graph says about real data.

The most important ideas are the five-number summary, the interquartile range, and the meaning of the median line inside the box. The box covers the middle $50\%$ of the data, from $Q_1$ to $Q_3$ . The formula $\text{IQR}=Q_3-Q_1$ measures the spread of the middle half of the data.

Outliers are often checked using $Q_1-1.5(\text{IQR})$ and $Q_3+1.5(\text{IQR})$ .

Key Facts

A box plot is built from the five-number summary: minimum, $Q_1$ , median, $Q_3$ , and maximum.
The median, also called $Q_2$ , divides the ordered data set into two halves.
The box extends from $Q_1$ to $Q_3$ and contains the middle $50\%$ of the data.
The interquartile range is $\text{IQR}=Q_3-Q_1$ .
The total range is $\text{range}=\text{maximum}-\text{minimum}$ .
A common outlier rule marks values below $Q_1-1.5(\text{IQR})$ or above $Q_3+1.5(\text{IQR})$ as possible outliers.
Longer whiskers or a longer side of the box show greater spread in that part of the data.
When comparing box plots, compare medians for center and compare $\text{IQR}$ or range for spread.

Vocabulary

Box plot: A graph that displays a data set using its five-number summary.
Five-number summary: The minimum, $Q_1$ , median, $Q_3$ , and maximum values of an ordered data set.
Median: The middle value of an ordered data set, or the average of the two middle values when there are an even number of values.
Quartile: A value that divides ordered data into fourths, such as $Q_1$ , $Q_2$ , and $Q_3$ .
Interquartile range: The spread of the middle half of the data, found with $\text{IQR}=Q_3-Q_1$ .
Outlier: A data value that is much smaller or much larger than most other values in the set.

Common Mistakes to Avoid

Confusing the median with the mean, which is wrong because a box plot shows the median, not the average.
Reading the box width as the number of data values, which is wrong because each quartile represents about $25\%$ of the data even if the spaces look different.
Forgetting to order the data before finding quartiles, which is wrong because $Q_1$ , the median, and $Q_3$ depend on position in the sorted list.
Using $\text{range}=Q_3-Q_1$ , which is wrong because $Q_3-Q_1$ is the $\text{IQR}$ , while range is $\text{maximum}-\text{minimum}$ .
Assuming a longer whisker means more data values, which is wrong because it means the values in that quartile are more spread out.

Practice Questions

1 For the data set $4, 6, 7, 9, 10, 12, 15$ , find the median, $Q_1$ , $Q_3$ , and $\text{IQR}$ .
2 A box plot has minimum $8$ , $Q_1=12$ , median $15$ , $Q_3=21$ , and maximum $30$ . Find the range and $\text{IQR}$ .
3 Using $Q_1=20$ and $Q_3=32$ , find the lower and upper outlier fences using $Q_1-1.5(\text{IQR})$ and $Q_3+1.5(\text{IQR})$ .
4 Two classes have the same median test score, but Class A has a much larger $\text{IQR}$ than Class B. Explain what this means about the consistency of the scores.

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Reading and Interpreting Box Plots Cheat Sheet

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