What a box plot summary tells you
A box plot condenses a list of numbers into five landmarks: the minimum, the first quartile (Q1), the median, the third quartile (Q3) and the maximum. Together they show where the data starts and ends, where the middle sits, and how widely the central half of the values is spread. Because each landmark is a rank-based statistic, the summary is not dragged around by a single extreme value the way an average can be.
Use this calculator when you want to compare groups, check a dataset for skew or outliers before running further tests, or produce the numbers you need to draw a box-and-whisker chart by hand. Paste values separated by commas, spaces, semicolons or new lines and the tool sorts them, reports the five-number summary, and flags any value outside the 1.5 × IQR fences.
How the quartiles and fences are computed
This calculator uses the median-of-halves method. Sort the data, find the median, split the list into a lower and an upper half, and take the median of each half. When the number of values is odd, the overall median is left out of both halves; when it is even, the list is simply cut in the middle. Other software (Excel's QUARTILE.INC, R's default type 7) interpolate between ranks and can differ slightly, especially for small samples.
Outliers are identified with Tukey's fences, which are built from the interquartile range:
- IQR = Q3 − Q1, the spread of the middle 50% of the data.
- Lower fence = Q1 − 1.5 × IQR; any value below it is flagged.
- Upper fence = Q3 + 1.5 × IQR; any value above it is flagged.
- n is the count of valid numbers; entries that are not numbers are ignored.
Worked example
Take the nine values 12, 5, 8, 30, 2, 9, 4, 11, 7. Sorted they read 2, 4, 5, 7, 8, 9, 11, 12, 30, so n = 9, the minimum is 2 and the maximum is 30. The middle (5th) value is 8, so the median is 8.
With n odd, the lower half is 2, 4, 5, 7 and its median is (4 + 5) / 2 = 4.5, so Q1 = 4.5. The upper half is 9, 11, 12, 30 and its median is (11 + 12) / 2 = 11.5, so Q3 = 11.5. The IQR is 11.5 − 4.5 = 7.
The fences are 4.5 − 1.5 × 7 = −6 and 11.5 + 1.5 × 7 = 22. The value 30 exceeds 22, so it is the single outlier, and the calculator reports exactly these numbers. Note that the upper whisker of a drawn plot would stop at 12, the largest value inside the fence, while 30 is plotted as a separate point.
Common mistakes and how to interpret the result
- Assuming every flagged point is an error. The 1.5 × IQR rule marks values that are unusual relative to the middle of the data. They may be genuine measurements, so investigate before deleting anything.
- Comparing quartiles from different software. A different quartile definition can shift Q1 and Q3 by a fraction of a unit on small samples. State the method you used when reporting results.
- Reading the box as the whole data range. The box covers only the middle half. If the median sits off-center in the box or one whisker is much longer, the distribution is skewed in that direction.
- Trusting the summary with very few values. With fewer than about eight points, quartiles are coarse and fences can flag or miss values almost arbitrarily.