📚 Practice With Worksheets
Practice creating and interpreting box-and-whisker plots with the resources below. The 🛠️ icon identifies a companion worksheet designed specifically for use with the interactive tool above.
▶️ Learn With Videos
Review the five-number summary, interquartile range, and how to connect a data set with its box plot.
🛠️ How to Use This Tool
Enter at least five numerical values separated by commas, spaces, tabs, or line breaks. Decimals and negative values are supported.
Add an optional plot title, select a box color, and choose Build Plot. You may also load the sample data or generate a random whole-number data set using a chosen sample size and range.
Examine the ordered data, five-number summary, count, range, and IQR. Select Export PNG to save the graph and summary for a presentation, report, or class project.
🧠 Things to Notice
The box extends from Q1 to Q3 and represents the middle 50% of the ordered data. The median divides that box into two sections.
Each quartile contains about 25% of the data, but the sections of the graph do not have to be the same length. Longer sections indicate greater spread.
Changing one extreme value may greatly affect the range and a whisker while having little or no effect on the median or IQR.
📘 Vocabulary
Box-and-Whisker Plot: A number-line display that shows the distribution of data using the five-number summary.
Five-Number Summary: The minimum, Q1, median, Q3, and maximum of a data set.
Minimum: The least value in an ordered data set.
Maximum: The greatest value in an ordered 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 data each.
Q1: The median of the lower half of an ordered data set.
Q3: The median of the upper half of an ordered data set.
Range: The difference between the maximum and minimum values.
Interquartile Range (IQR): The difference between Q3 and Q1; it measures the spread of the middle 50% of the data.
Variability: The amount of spread or dispersion within a data set.
📐 Building and Interpreting a Box Plot
Order the data first. Find the median, then find Q1 from the lower half and Q3 from the upper half. When the number of values is odd, this tool does not include the overall median in either half.
\(\text{Five-number summary: Minimum,\ Q1,\ Median,\ Q3,\ Maximum}\)
The range describes the full spread from the smallest value to the largest value.
\(\text{Range}=\text{Maximum}-\text{Minimum}\)
The IQR describes the spread of the middle half of the data and is less affected by extreme values than the range.
\(\text{IQR}=Q3-Q1\)
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