Quartile & IQR Calculator
Quartile & IQR Calculator
Enter a list of numbers to instantly calculate its three quartiles (which split the sorted data into four equal groups) and the interquartile range — the span of the middle 50% of the data.
Q1, Q2, and Q3 correspond to the 25th, 50th, and 75th percentiles respectively — Q2 is simply another name for the median. The interquartile range (Q3 minus Q1) captures the spread of the middle half of the data while ignoring the extreme top and bottom quarters, which makes it far less sensitive to outliers than the full range (max minus min). IQR is also the basis for the standard 1.5×IQR outlier-detection rule used throughout statistics and in box-plot construction.
- Q1, Q2, Q3: the 25th, 50th, and 75th percentiles respectively — Q2 is the same as the median.
- IQR formula: Interquartile Range = Q3 − Q1 — the range covering the middle half of the data, unaffected by extreme outliers at either end.
- Why IQR matters: it's the basis for the standard 1.5×IQR outlier detection rule and for drawing box plot whiskers.
Why use IQR instead of range for measuring spread?
Range only looks at the two most extreme values, so a single outlier can distort it — IQR describes the spread of the middle, typical data and ignores extreme values entirely.
Is Q2 always exactly the same as the median from a Mean/Median/Mode calculator?
Yes — Q2 is defined as the 50th percentile, which is identical to the median by definition, regardless of which tool calculates it.
Quartile & IQR Calculator
Enter a list of numbers to instantly calculate its three quartiles (which split the sorted data into four equal groups) and the interquartile range — the span of the middle 50% of the data.
Q1, Q2, and Q3 correspond to the 25th, 50th, and 75th percentiles respectively — Q2 is simply another name for the median. The interquartile range (Q3 minus Q1) captures the spread of the middle half of the data while ignoring the extreme top and bottom quarters, which makes it far less sensitive to outliers than the full range (max minus min). IQR is also the basis for the standard 1.5×IQR outlier-detection rule used throughout statistics and in box-plot construction.
- Q1, Q2, Q3: the 25th, 50th, and 75th percentiles respectively — Q2 is the same as the median.
- IQR formula: Interquartile Range = Q3 − Q1 — the range covering the middle half of the data, unaffected by extreme outliers at either end.
- Why IQR matters: it's the basis for the standard 1.5×IQR outlier detection rule and for drawing box plot whiskers.
Why use IQR instead of range for measuring spread?
Range only looks at the two most extreme values, so a single outlier can distort it — IQR describes the spread of the middle, typical data and ignores extreme values entirely.
Is Q2 always exactly the same as the median from a Mean/Median/Mode calculator?
Yes — Q2 is defined as the 50th percentile, which is identical to the median by definition, regardless of which tool calculates it.