Turn a list of numbers into its five-value summary and a simple box plot. The method is stated so the quartiles are reproducible.
For 1, 2, 3, 4, 5, the five numbers are 1, 1.5, 3, 4.5, and 5. The lower and upper halves exclude the middle value.
Ordered from minimum to maximum.
Whiskers: minimum to maximum. Box: Q1 to Q3.
How to Calculate a Five-Number Summary
Enter at least two observations. The calculator sorts them numerically, then reports the minimum, lower quartile (Q1), median (Q2), upper quartile (Q3), and maximum. The result card also shows a box plot, the full range, and the interquartile range (IQR). Use the presets to inspect how an odd count, an even count, negative values, and repeated values change the summary.
Copy the five reported numbers with their labels when you need to cite the result. A five-number summary describes the distribution of one numeric dataset; it does not describe two-variable correlation or establish statistical significance.
Which Quartile Method Does This Tool Use?
This tool uses the median-of-halves, or exclusive-median, convention. First find the overall median. For an odd number of observations, leave that middle observation out of both halves. For an even number, split the ordered list evenly. Q1 is the median of the lower half, and Q3 is the median of the upper half.
Software packages and textbooks use several quartile conventions, especially for small datasets. The same observations can therefore yield different Q1 and Q3 values under a different convention. Compare methods before treating a discrepancy as an error. This page keeps the method fixed; our separate Quartile & IQR tool focuses on quartile spread and outlier fences.
Worked Example With Five Values
Sort 1, 2, 3, 4, 5. The minimum is 1 and the maximum is 5. The middle observation is 3, so the median is 3. Exclude 3: the lower half is 1, 2 and the upper half is 4, 5. Their medians are (1 + 2)/2 = 1.5 and (4 + 5)/2 = 4.5. The summary is 1, 1.5, 3, 4.5, 5. The range is 5 − 1 = 4; the IQR is 4.5 − 1.5 = 3.
How to Read the Box Plot
The left whisker marks the minimum and the right whisker marks the maximum. The box spans Q1 through Q3, and its internal line marks the median. The box therefore covers the central half of the ordered observations under this quartile convention. A wide box indicates more spread in that middle portion; a narrow box indicates less.
This compact visual draws whiskers to the actual minimum and maximum. Some statistical box plots instead stop whiskers at the most extreme non-outlier observations and draw outliers separately. Do not infer outlier status from this page’s whiskers.
What the Five Values Do and Do Not Tell You
The summary identifies the center and spread without showing every observation. It helps compare distributions that have different medians or IQRs. It does not reveal all clusters, gaps, modes, or repeated values. Two datasets can share the same five values but look different when plotted point by point.
A dataset with all values equal has a zero range and zero IQR. That is valid. A dataset with only two observations still has five reported positions because Q1 equals the minimum and Q3 equals the maximum under this method.
Five-Number Summary FAQs
What are the five numbers?
Minimum, first quartile (Q1), median, third quartile (Q3), and maximum.
Is Q2 the median?
Yes. Q2 is the median of the full ordered dataset.
Why does my spreadsheet show different quartiles?
It may use a percentile-interpolation method rather than the median-of-halves method stated here.
Can the IQR be zero?
Yes. Q1 and Q3 can be equal when the central observations are identical.
Editorial review
SolverCalc names Prof. Dr. Khalil Mudassar as its educational reviewer. The formulas and examples on this page follow the references below.
Sources
Disclaimer
For educational use. Check your class or textbook convention when the problem defines a different range, sequence index, or notation.