Box Plot Calculator
Find the five-number summary and IQR for a box plot.
A box plot displays the median, quartiles and spread of a data set.
How the Math Works
The Box Plot Calculator computes the five-number summary (minimum, Q1, median, Q3, maximum) using linear interpolation for quartile determination. For a dataset sorted in ascending order, the median splits the data into two halves. Q1 and Q3 are found by calculating the median of the lower and upper halves respectively, with linear interpolation resolving fractional positions. The Interquartile Range (IQR) is then derived as Q3 minus Q1, measuring the spread of the middle 50% of data points without distortion from outliers.
Practical Applications
To use this calculator, input your raw numerical dataset into the provided field and submit. The tool will instantly process your data to display the five-number summary and IQR, which are essential for constructing a box plot. This is particularly useful when analyzing experimental results, survey responses, or quality control metrics where visual data representation and outlier detection are required for informed decision-making.
Day-to-Day Use
Understanding your data's distribution through box plots helps you grasp what's typical versus extreme in everyday scenarios. Whether evaluating household expense patterns, assessing sports performance consistency, or comparing product reviews, the box plot reveals the central tendency and variability at a glance. This insight helps identify unusual values that might signal errors, opportunities, or areas needing attention in both personal and professional contexts.
Worked example
4, 8, 15, 16, 23, 42 → median 15.5, IQR 14.75.
FAQ
What are the whiskers?
They extend to the furthest points within 1.5×IQR of the quartiles.