IQR & Quartile Calculator
Math CalculatorsQ1/Q2/Q3, IQR, outlier fences
Quick Answer
IQR & Quartile Calculator: Q1/Q2/Q3, IQR, outlier fences. IQR & Quartile Calculator uses standard math formulas to compute accurate results instantly.
IQR = Q3 − Q1
6
Q1=3, Q3=9, n=9
Q1 (25%)3
Median Q27
Q3 (75%)9
Range14
Lower fence-6
Upper fence18
Outliers (1.5×)None
Extreme (3×)None
Calculation steps
- 1Sort: 1, 3, 3, 6, 7, 8, 9, 12, 15 (n=9)
- 2Q2 position = (n−1)×0.5 = 4.00 → median = 7
- 3Q1 position = (n−1)×0.25 = 2.00 → Q1 = 3 (linear interpolation)
- 4Q3 position = (n−1)×0.75 = 6.00 → Q3 = 9
- 5IQR = 9 − 3 = 6; fences = [-6, 18]
Percentile interpretation
| Stat | Meaning |
|---|---|
| Q1 25% | 25% of data below this |
| Median 50% | Half below, half above; robust to outliers |
| Q3 75% | 75% of data below this |
| IQR | Middle 50% spread; robust dispersion measure |
| 1.5×IQR fence | Tukey's boxplot outlier rule |
💡 IQR beats standard deviation for skewed data (incomes, house prices): one billionaire doesn't move the IQR at all. Quartile methods differ across tools — this uses linear interpolation (Excel PERCENTILE.INC / NumPy default); Tukey hinges may differ slightly.
Was this tool helpful?
How to Use
- Enter values or expressions: type directly into the IQR & Quartile Calculator — keyboard friendly.
- Instant results: everything computes live as you type, no button needed.
- Follow the steps: the result panel shows full working and formula substitution.
- Copy or recompute: one-click copy; change any input to recalculate instantly.
Key Points
- IQR & Quartile Calculator is a free online math tool — open and use, no sign-up.
- All calculations run locally in your browser; your data never leaves the device.
- Key capability: Q1/Q2/Q3, IQR, outlier fences.
- Results come with formulas and reference tables so you can verify every number.
Formula & How It Works
IQR & Quartile Calculator formula
IQR & Quartile Calculator uses standard math formulas to compute accurate results instantly.
FAQ
How do I use the IQR & Quartile Calculator?
Open the page and fill in the input fields — results update automatically. Q1/Q2/Q3, IQR, outlier fences.
Are the results accurate?
Yes. All calculations use standard mathematical formulas and are verified for accuracy.
Is it free? Do I need to sign up?
Completely free. No registration, login or download required — just open and use.
Does it work on mobile?
Yes. The responsive design works on phones, tablets and desktops.
Is my data saved?
No. All calculations run locally in your browser. Nothing is uploaded or stored.
Related Tools
HOT
Basic Calculator
Add, subtract, multiply, divide with full keyboard supportHOTScientific Calculator
Trig, log, exponent, factorial · DEG/RAD modesHOTPercentage Calculator
Percent of, percentage share, and percent changeFraction Calculator
Add, subtract, multiply, divide fractions with simplificationHOTNumber Base Converter
Convert between binary, octal, decimal and hexadecimalPermutation & Combination Calculator
Permutations A(n,m) and combinations C(n,m)Random Number Generator
Custom range, integers or decimals, batch generationPrime Number Tools
Primality test, prime factorization and prime listsRelated Guides
Source & Updates
Standard mathematical formulas. All logic verified. Last updated: 2025-07
Last updated:
Formulas and content on this page are reviewed by the YiJianSuan team. For reference only — official sources prevail.
Maintained and periodically reviewed by the YiJianSuan editorial team — review process in ourEditorial Policy.
Cite this page: YiJianSuan. IQR & Quartile Calculator[EB/OL]. https://www.yijiansuan.com/en/c/math/iqr-quartile
Results provided by this tool are for reference only and do not constitute professional advice.