Interquartile Range Calculator
Calculate Q1, Q3, and the interquartile range (IQR) from a data set, and flag outliers using the 1.5×IQR rule.
Result
Interquartile Range (IQR)
7.00
Q1 (25th percentile)
36.00
Q3 (75th percentile)
43.00
Outliers (1.5×IQR rule)
7, 15
How to Use the Interquartile Range Calculator
Enter a list of numbers separated by commas or new lines. The calculator sorts the data, splits it into a lower half and an upper half around the median, then finds the median of each half — the first quartile (Q1) and third quartile (Q3). The interquartile range (IQR) is the spread between them, and it's also used to flag statistical outliers using the standard 1.5×IQR rule.
Outlier if value < Q1 − 1.5×IQR or value > Q3 + 1.5×IQR
Example
For the data set 7, 15, 36, 39, 40, 41, 42, 43, 47, 49 (already sorted), the lower half is 7, 15, 36, 39, 40 (Q1 = 36) and the upper half is 41, 42, 43, 47, 49 (Q3 = 43), giving an IQR of 43 − 36 = 7. The lower fence is 36 − 1.5×7 = 25.5, so 7 and 15 are flagged as outliers.
Common Use Cases
- Identifying outliers in a data set before further statistical analysis.
- Measuring the spread of the middle 50% of data, which is less sensitive to extreme values than the full range.
- Building box plots or summarizing data distributions for a report.
FAQs
- How is Q1 and Q3 calculated here? This calculator uses the common exclusive method: sort the data, split it into a lower half and upper half around the median (excluding the median itself when the count is odd), then Q1 is the median of the lower half and Q3 is the median of the upper half. Other methods (like linear interpolation) can give slightly different results for the same data.
- Why 1.5×IQR for flagging outliers? It's a widely used statistical convention (originating with box plots) that flags values falling far enough outside the middle 50% of the data to be considered unusual, without being so strict that normal variation gets flagged.
- What's the minimum data set size this works with? You need at least 4 numbers to get a meaningful Q1/Q3 split — with fewer values, quartiles aren't well-defined and the calculator won't produce a result.