Outlier Calculator

An outlier is a data value that sits far away from the bulk of the other values in a data set. Outliers can arise from genuine extreme observations (a very tall person in a height survey), from measurement error, or from data entry mistakes. Identifying them matters because a single outlier can dramatically shift summary statistics like the mean and standard deviation, making your analysis misleading. The IQR method, also called the Tukey fences method, is one of the most widely taught and robust approaches to outlier detection. It works by computing the interquartile range (IQR = Q3 minus Q1, the spread of the middle 50% of the data) and then setting two boundaries called fences. The lower fence is Q1 minus 1.5 times the IQR. The upper fence is Q3 plus 1.5 times the IQR. Any value that falls outside these fences is classified as a potential outlier. Because the fences are built from the middle of the distribution rather than from the extremes, they are not themselves distorted by the very outliers they are trying to detect. That makes the IQR method more appropriate than standard deviation methods for skewed distributions. This calculator accepts a comma-separated list of numbers, computes Q1, Q3, and IQR using linear interpolation, then applies the 1.5 x IQR rule. It returns the lower and upper fences, a list of any outlying values found, the total data count, and the count of clean (non-outlier) values. It is useful for students, data analysts, teachers, and anyone cleaning a data set before further statistical analysis.

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100
outliers detected
Lower fence-3.00
Upper fence13.00
IQR4.00
Q13.00
Q37.00
Clean values6

How it works

The calculator sorts the data and uses linear interpolation to compute Q1 (25th percentile) and Q3 (75th percentile). IQR = Q3 minus Q1. Lower fence = Q1 minus 1.5 times IQR. Upper fence = Q3 plus 1.5 times IQR. Every data value below the lower fence or above the upper fence is listed as a potential outlier. The clean count is the total number of values minus the number of outliers.

Worked example

Data: 2, 3, 4, 5, 6, 7, 100 (n = 7, sorted). Q1 rank = 0.25 x 8 = 2.0 (exact), so Q1 = sorted[1] = 3.00. Q3 rank = 0.75 x 8 = 6.0 (exact), so Q3 = sorted[5] = 7.00. IQR = 7 - 3 = 4.00. Lower fence = 3 - 1.5 x 4 = -3.00. Upper fence = 7 + 6 = 13.00. The value 100 exceeds the upper fence of 13.00 and is the only outlier. 6 clean values remain. These match the default values pre-filled above.

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Frequently asked questions

How does the IQR method detect outliers?

The IQR method calculates the interquartile range (Q3 minus Q1) and then sets fences at Q1 minus 1.5 times IQR (lower fence) and Q3 plus 1.5 times IQR (upper fence). Any value below the lower fence or above the upper fence is flagged as a potential outlier. This approach is robust because the fences are based on the middle 50% of the data rather than the extreme values.

Is the IQR outlier method the same as the Z-score method?

No. The Z-score method flags values that are more than a certain number of standard deviations from the mean (typically 2 or 3). The IQR method uses quartiles and is more resistant to outliers themselves distorting the calculation, which makes it better suited to skewed data or distributions with heavy tails.

Should I always remove outliers?

Not necessarily. Outliers can represent genuine extreme values that are part of the true distribution, or they can indicate data entry errors, measurement mistakes, or a genuinely unusual observation. Always investigate the cause of an outlier before deciding whether to remove it or treat it separately in your analysis.