Updated · Built and checked by the PlinzoTools team, formulas tested against published sources
Calculate the range and interquartile range (IQR) of a data set.
Range and interquartile range (IQR) are two common measures of spread. Range is the simplest (max minus min); IQR is more robust to outliers since it only looks at the middle 50% of the data (the same measures used to draw a boxplot).
Enter your data set. Range, Q1, Q3, and IQR all appear instantly.
Range = Max - Min
IQR = Q3 - Q1, where Q1 and Q3 are the 25th and 75th percentiles (linear interpolation method)
Take ten hypothetical values: 1, 2, 3, 4, 5, 6, 7, 8, 9, 100. The last value is deliberately extreme.
Range = 100 - 1 = 99
Q1 index = 0.25 × 9 = 2.25, between 3 and 4, so Q1 = 3 + 0.25 × 1 = 3.25
Q3 index = 0.75 × 9 = 6.75, between 7 and 8, so Q3 = 7 + 0.75 × 1 = 7.75
IQR = 7.75 - 3.25 = 4.5
The range of 99 says the data is spread across nearly a hundred units, but the IQR of 4.5 shows that the middle half of the values sits in a narrow band. The gap between those two answers is a strong hint that at least one extreme value is present. If you remove the 100, the range drops to 8 while the IQR barely moves.
The page mentions that boxplots flag values beyond 1.5 times the IQR from the quartiles. You can apply the same rule with the results from the tool.
Any value below -3.5 or above 14.5 would be flagged as a potential outlier. In this example, only 100 qualifies. Flagging does not mean the value is wrong. It is a prompt to check whether it is a typo, a measurement error, or a genuine but unusual observation. Deleting data because of a rule alone is not good practice.
The tool sorts your values and finds Q1 and Q3 by linear interpolation, the same way the Percentile Calculator does at 25 and 75. This matches Excel's QUARTILE.INC. Other textbooks split the data into halves and take the median of each half, which can produce slightly different quartiles, particularly for small data sets. If you are comparing against a class answer key, check which method it expects.
Range is entirely determined by the two most extreme values, so a single outlier can distort it. IQR only looks at the middle half of the data, making it much more resistant to outliers.
It's the standard basis for the "whiskers" and outlier detection in a boxplot -- values more than 1.5×IQR beyond Q1 or Q3 are commonly flagged as outliers.
Yes. If at least half of your values are identical around the middle, Q1 and Q3 can be equal, giving an IQR of 0, even when the range is not zero.
No. The IQR covers only the middle part of the data, so it can never exceed the range, which covers everything.
Different quartile methods exist. This tool uses linear interpolation, while some textbooks take the median of each half of the data. The two can differ for small data sets.
No. The fences only flag potential outliers. Investigate before deciding whether to keep or remove them.
Reference: NIST Weights and Measures