Quartile and IQR calculator splits your dataset into four parts and reports the interquartile range — the spread of the middle 50% of values.
About this calculator
Quartile and IQR calculator splits your dataset into four parts and reports the interquartile range — the spread of the middle 50% of values. Outliers stand apart from this middle band, which makes IQR more robust than range when a few extreme values exist.
Students use quartiles for box-and-whisker plots in CBSE and ICSE statistics units. Analysts use IQR to describe salary distributions where a few crore packages skew the mean. The calculator also flags values outside the 1.5×IQR fences used in standard outlier rules.
Combine with [[percentile]] for custom ranks, [[mean-median-mode]] for averages, and [[z-score]] when you need standard-deviation-based outlier checks. For larger samples see [[standard-deviation]].
Common uses
- Drawing a box plot for CBSE Class 10 statistics homework
- HR analyst reporting salary quartiles without revealing individual pay
- Detecting outlier sales days in a kirana shop
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Frequently asked questions
What is the interquartile range and why use it instead of range?
IQR is Q3 minus Q1 — the spread of the middle half of data. Range (max minus min) is distorted by one extreme value. IQR ignores the top and bottom 25%, so it describes typical spread better.
How do you find outliers using IQR?
Compute fences: lower = Q1 − 1.5×IQR, upper = Q3 + 1.5×IQR. Values outside these fences are outliers by the Tukey rule. This calculator reports how many values fall outside.
Is Q2 the same as the median?
Yes. Q2 is the 50th percentile — the middle value when data is sorted. For an even count, it is the average of the two middle values.
How do quartiles help compare income data in India?
Mean income is pulled up by billionaires. Quartiles show the median earner (Q2) and the spread of the middle 50% (IQR). Reporting Q1, median, and Q3 gives a fairer picture than mean alone.