Outlier calculator
Paste your numbers separated by commas, spaces or new lines and choose a rule. The tool lists the values outside the limits, shows the limits it used and gives the data set without them.
Runs in your browser: nothing you enter is sent anywhere.
How to use it
- Paste the numbers.
- Choose the IQR rule or the z-score rule and, if you wish, change the multiplier or cut-off.
- Read the outliers, the limits and the cleaned list.
How it works
IQR rule: the tool sorts the data, finds Q1 and Q3 by the chosen method and flags values outside Q1 − k × IQR and Q3 + k × IQR. Z-score rule: it flags values whose distance from the mean is more than the cut-off times the sample standard deviation. The limits shown are mean ± cut-off × s.
Worked example
12, 14, 15, 15, 16, 17, 18, 19, 21, 48. By the median-of-halves method Q1 = 15 and Q3 = 19, so IQR = 4 and the fences are 15 − 6 = 9 and 19 + 6 = 25. Only 48 lies outside.
Tips
- Use the z-score rule on roughly bell-shaped data with many values; the IQR rule copes better with skewed data and small samples.
- For the full five-number summary and a picture, use the quartile calculator or box plot maker.
Frequently asked questions
What is the 1.5 × IQR rule?
Tukey's fences. The interquartile range is IQR = Q3 − Q1. A value below Q1 − 1.5 × IQR or above Q3 + 1.5 × IQR is flagged as an outlier. Box plots draw their whiskers and dots from the same rule.
Which quartile method should I use?
Quartiles are defined several ways and the fences move slightly with the method. The default, the median of each half with the middle excluded, is the textbook one; the interpolated method matches Excel's QUARTILE.INC.
How is the z-score computed?
z = (x − mean) / s, using the sample standard deviation s with n − 1 in the divisor. The extreme values also pull the mean and s, so in small samples a z-score rule can miss a clear outlier.
Should I delete outliers?
Not automatically. An outlier can be a typing error or a real, informative case. Check the source first and report what you removed.