Quartile Calculator: Analyze Data Distribution with Ease | Free Online Tool
The online quartile calculator sorts your numbers, pinpoints Q1 (25 %), Q2 (50 %), Q3 (75 %) and the inter-quartile range in one click; values beyond Q1 ± 1.5 × IQR flag potential outliers—a rule introduced by McGill et al. (1978) and still standard today (McGill, Tukey & Larsen, 1978).
Quartile Calculator
Results
First Quartile (Q1)
Second Quartile (Median, Q2)
Third Quartile (Q3)
Interquartile Range (IQR)
Box Plot
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How to use the tool
Paste your numbers
• Example A: 3, 8, 12, 20, 25, 30
• Example B: 45 50 55 60 80 90 100 110 130
Pick a method
• Inclusive keeps the median inside Q1/Q3.
• Exclusive drops the median.
• Percentile rounds to the nearest percentile index.
(Optional) Tick “Include Visualization” to see a box-plot.
Press “Calculate” to display Q1, Q2, Q3 and IQR. Out-of-range points appear as outliers on the plot.
The 1.5 × IQR outlier rule comes from box-plot inventor John Tukey (Tukey, 1977).
ISO 3534-1:2006 standardises quartile terminology (ISO, 2006).
“Box plots summarise a distribution in five numbers” (McGill, Tukey & Larsen, 1978).
NIST recommends ≥20 observations for stable quartile estimates (NIST, 2023).
FAQ
What is the difference between inclusive and exclusive quartiles?
Inclusive quartiles treat the median as part of both halves, so Q1 and Q3 can sit closer to the centre; exclusive quartiles drop the median, widening Q1-Q3 spacing (Hyndman & Fan, 1996).
How does the calculator flag outliers?
It marks any value below Q1 − 1.5 × IQR or above Q3 + 1.5 × IQR, the rule popularised by Tukey’s box-plot paper (Tukey, 1977).
Can I trust quartiles with fewer than five points?
You can compute them, but NIST warns that quartile estimates stabilise only after ~20 observations (NIST/SEMATECH, 2023).
Does the tool assume normal distribution?
No. Quartiles are non-parametric; they work for skewed or bimodal data because they depend solely on order statistics (Wilcox, 2012).
How are ties handled?
If duplicate numbers appear, they occupy consecutive positions in the sorted list; interpolation still proceeds normally, so quartiles stay valid (Wikipedia “Quartile”).
Why does the percentile method round indices?
The script matches Excel’s PERCENTILE.EXC behaviour, selecting the nearest ranked value instead of interpolating (Microsoft Docs, 2023).
Is IQR related to standard deviation?
For normal data, IQR ≈ 1.349 × σ, giving a quick σ estimate when outliers skew SD (Montgomery, 2017).
What is a “five-number summary”?
Minimum, Q1, median, Q3, and maximum—“a simple description of spread and centre” (Tukey, 1977).
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