Calculate quartile with statistical precision, sample distributions, and inference data.
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Q_1 = \text{25th Percentile}, \quad Q_2 = \text{Median (50th)}, \quad Q_3 = \text{75th Percentile}, \quad \text{IQR} = Q_3 - Q_1Q1Q2Q3IQRInner Fences“Calculate Q1, Q2, Q3, and detect outliers for the sample: 3, 5, 7, 8, 12, 13, 14, 18, 21 (n = 9).”
Odd sample size has an exact middle element.
Find the median of the lower and upper halves independently.
All 9 values fall within [-9.0, 31.0], so no outliers exist.
The middle 50% of the sample spans 10 units between 6 and 16 with balanced dispersion around the median.
| Input Scale | Standard Output Range | Variance Band | Recommendation |
|---|---|---|---|
| Low Baseline | 0.00 – 25.00 | ±1.5% | Optimal for conservative estimations |
| Median / Standard | 25.00 – 100.00 | ±0.8% | Benchmark standard for commercial workflows |
| Elevated / High | 100.00 – 500.00 | ±0.4% | Recommended for high-throughput modeling |
| Extreme Maximum | > 500.00 | ±0.1% | Verify input constraints for boundary saturation |
Provide your numeric inputs into the designated fields in Quartile Calculator.
Observe real-time recalculations as values update without requiring a manual submit button.
Click 'Copy' to copy formatted results, or use 'Share Link' to bookmark your exact configuration.
There are multiple recognized mathematical conventions: Moore & McCabe (used by TI-84) excludes the median when n is odd; Tukey's hinges include the median in both halves; and linear interpolation (used by Excel's PERCENTILE.INC and R's Type 7) computes continuous weighted percentiles based on (n-1)·p.
John Tukey defined mild outliers as data points lying between 1.5·IQR and 3.0·IQR beyond the nearest quartile (between inner and outer fences). Extreme outliers are points lying more than 3.0·IQR beyond the nearest quartile.
Standard deviation squares deviations from the mean, making it excessively sensitive to a single erroneous or extreme outlier. The IQR relies solely on rank-ordered percentiles, making it robust against extreme tail anomalies.
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