📚 Practice With Worksheets
Practice creating, reading, and comparing box-and-whisker plots with data involving student heights, test scores, and other middle school statistics contexts.
▶️ Learn With Videos
Review the five-number summary, calculate the IQR, and connect an ordered data set to its matching box plot.
🛠️ How to Use This Tool
Enter at least five values for each group using commas, spaces, tabs, or line breaks. Name each data set and choose a color for each plot.
Add an optional overall title and axis label, then choose Build Comparative Plot. Use the checkboxes to show or hide Data Set 1, Data Set 2, or the combined data.
Compare the box plots, summaries, ordered data, medians, IQRs, ranges, and overlap. Select Export PNG to save the visible graph and summaries for a report, slideshow, or class project.
🧠 Things to Notice
The medians compare the centers of the two groups, while the IQRs compare how spread out the middle 50% of each group is.
Boxes that overlap share some values within their middle 50%, but overlap alone does not mean the two distributions are identical.
The combined box plot summarizes all values together. Its median and quartiles do not have to fall halfway between the corresponding values of the two original groups.
📘 Vocabulary
Comparative Box Plot: Two or more box plots displayed on the same number line so their distributions can be compared.
Five-Number Summary: The minimum, Q1, median, Q3, and maximum of a data set.
Median: The middle value, or mean of the two middle values, in an ordered data set.
Quartile: A boundary that divides ordered data into four groups containing about 25% of the values each.
Interquartile Range (IQR): The difference between Q3 and Q1; it measures the spread of the middle 50% of a data set.
Range: The difference between the maximum and minimum values.
Variability: The amount of spread or dispersion in a data distribution.
Overlap: A shared interval occupied by parts of two distributions on the same scale.
Distribution: The way data values are spread across a number line.
Center: A value used to describe the typical location of a distribution; the median is the center shown by a box plot.
Combined Data: One data set formed by joining all values from two or more groups.
📐 Comparing Box-and-Whisker Plots
Compare center. The group with the greater median has a distribution centered farther to the right on the shared number line.
Compare the middle 50%. A larger IQR means the values between Q1 and Q3 are more spread out.
\(\text{IQR}=Q3-Q1\)
Compare the full spread. A larger range means the complete data set extends across a wider interval.
\(\text{Range}=\text{Maximum}-\text{Minimum}\)
Consider overlap. Overlapping boxes show that portions of the middle 50% occupy the same interval. Little or no overlap can indicate a clearer separation between the groups.
Use several features together. A strong comparison should discuss center, variability, range, overlap, and the context of the data rather than relying on only one number.
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