ganak.appQuartile Calculator
Free quartile calculator. Enter data to find Q1, Q2, Q3, five-number summary, IQR, and percentiles. Compare 3 methods with step-by-step solution and box plot.
Supports commas, spaces, tabs, or new lines. Paste from spreadsheets works too.
Five-Number Summary
Min, Q1, Median, Q3, Max with key metrics
Box & Whisker Plot
Visual distribution with quartile boundaries
Method Comparison
Same data, three quartile methods — see why results differ
| Method | Q1 | Median | Q3 | IQR |
|---|---|---|---|---|
| Exclusive (Tukey) selected | 15.00 | 40.00 | 43.00 | 28.00 |
| Inclusive (Excel INC) | 25.50 | 40.00 | 42.50 | 17.00 |
| Interpolation (Excel EXC) | 15.00 | 40.00 | 43.00 | 28.00 |
Methods produce different results because there is no universally agreed-upon definition for quartiles. Differences are largest for small datasets and converge as n increases.
Percentile & Decile Finder
Find the value at any percentile. P25 and P75 match Q1 and Q3 from the selected method. Other percentiles use linear interpolation (PERCENTILE.INC).
Deciles (D1–D9)
Step-by-Step Solution
How the quartiles are calculated using the Exclusive (Tukey) method
Step 1: Sort the data in ascending order
n = 11 values
Step 2: Find the median (Q2)
Median = 40.00
With 11 values (odd), the median is the middle value at position 6. Median = 40.00
Step 3: Find Q1 (first quartile)
Q1 = 15.00
Lower half = first 5 values. Q1 = median of lower half = 15.00
Step 4: Find Q3 (third quartile)
Q3 = 43.00
Upper half = last 5 values. Q3 = median of upper half = 43.00
Step 5: Calculate IQR = Q3 − Q1
IQR = 43.00 − 15.00 = 28.00
The interquartile range is 28.00. This means the middle 50% of your data spans 28.00 units.
Step 6: Outlier fences (Tukey method)
Fences: [-27.00, 85.00]
Lower fence = Q1 − 1.5 × IQR = 15.00 − 42.00 = -27.00
Upper fence = Q3 + 1.5 × IQR = 43.00 + 42.00 = 85.00
All values fall within the fences — no outliers detected.
What Are Quartiles?
Dividing data into four equal parts
Quartiles are values that divide an ordered dataset into four equal groups, each containing 25% of the data. There are three quartiles:
- Q1 (First Quartile / 25th Percentile) — 25% of the data falls below this value. Also called the lower quartile.
- Q2 (Second Quartile / Median / 50th Percentile) — the middle value that splits the data in half.
- Q3 (Third Quartile / 75th Percentile) — 75% of the data falls below this value. Also called the upper quartile.
Example
Dataset: 3, 7, 8, 12, 13, 18, 21
Q1 = 7 | Median = 12 | Q3 = 18 | IQR = 18 − 7 = 11
Together with the minimum and maximum, the three quartiles form the five-number summary — a compact description of a dataset that is the foundation for box plots and outlier detection.
How to Calculate Quartiles Step by Step
The complete quartile calculation process
- Sort the data in ascending order (smallest to largest).
- Find the median (Q2) — the middle value. For an even count, average the two middle values.
- Find Q1 — the median of the lower half of the data (all values below Q2).
- Find Q3 — the median of the upper half of the data (all values above Q2).
- Calculate IQR = Q3 − Q1 — the interquartile range measures the spread of the middle 50%.
Quartile Formulas
Q1 position = (n + 1) / 4
Q2 position = (n + 1) / 2
Q3 position = 3(n + 1) / 4
IQR = Q3 − Q1
When a quartile position falls between two data points, interpolation is used. The exact method of interpolation varies — which is why different tools can give slightly different quartile values for the same dataset.
Why Different Quartile Methods Exist
Understanding Exclusive, Inclusive, and Interpolation methods
There is no single universally agreed-upon formula for quartiles. Different textbooks, software, and calculators use different conventions. This calculator supports the three most common methods so you can match the one used by your course, exam, or software.
Exclusive (Tukey)
Splits data at the median and excludes it for odd n. Takes the median of each half. Most common in statistics textbooks and AP Statistics.
Inclusive (Excel INC)
Uses linear interpolation at p×(n−1). This is Excel's default QUARTILE.INC and NumPy's default. Includes endpoints in the calculation.
Interpolation (Excel EXC)
Uses interpolation at p×(n+1) excluding endpoints. Matches Excel QUARTILE.EXC. Requires at least 4 data points.
For most practical purposes, the differences are small — especially with larger datasets. If you are getting a different answer than your textbook, try switching methods. Use the Method Comparison table above to see all three results side by side.
Practical Uses of Quartiles
Where quartiles matter beyond the classroom
Salary & Compensation
- • Q1 = entry-level salary range
- • Median = typical mid-career pay
- • Q3 = senior/high-performer compensation
- • Used to benchmark pay equity
Standardized Testing
- • Scores in Q1 may need intervention
- • Q3+ identifies advanced learners
- • IQR measures score consistency
- • Used by SAT, GRE, GMAT reporting
Finance & Investing
- • Stock return distributions
- • Risk assessment (spread of returns)
- • Real estate price ranges by market
- • Portfolio performance benchmarks
Healthcare & Research
- • Patient vitals normal ranges
- • Drug response distributions
- • Growth charts (pediatric percentiles)
- • Identifying outlier lab results
Quartiles are preferred over mean-based statistics when data is skewed or contains outliers. Income data, for example, is heavily right-skewed — the median and quartiles give a much more accurate picture of typical earners than the mean does.
Frequently Asked Questions
Common questions about calculating quartiles, methods, and interpreting results
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Last updated Apr 13, 2026