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Quartile Calculator

Calculate Q1, Q2, Q3, IQR, and the five-number summary. Interactive box plot, outlier detection, step-by-step solution, and three quartile methods.

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Separate values with commas, spaces, or new lines

Excludes the median when computing Q1 and Q3. Most common in statistics textbooks.

Quick Examples
Quick Summary
—
IQR (Interquartile Range)
Q1 (25th pct)—
Q2 / Median—
Q3 (75th pct)—
n—
Methods Explained
Inclusive (Moore-McCabe): Splits the sorted data excluding the median. Q1 = median of lower half, Q3 = median of upper half.
Exclusive (Tukey): Includes the median in both halves. Often used in exploratory data analysis.
Midpoint (Excel): Uses interpolation — same as Excel's QUARTILE function. L = (n+1)×p/4.
Key Formulas
Q2 (Median)middle value
IQRQ3 − Q1
Lower fenceQ1 − 1.5×IQR
Upper fenceQ3 + 1.5×IQR
Extreme lowQ1 − 3×IQR
Extreme highQ3 + 3×IQR
Interpretation
Q1 — 25% of data falls below this value
Q2 — Median; 50% of data falls below
Q3 — 75% of data falls below this value
IQR — Spread of the middle 50% of data; robust to outliers
Whiskers — Extend to the most extreme non-outlier values