Quartile & IQR Calculator

Find Q1, Q2 (median), Q3, IQR, and the five-number summary — with full step-by-step workings for FBISE, CBSE, IGCSE, O Levels, A Levels & IB.

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At least 4 values recommended for meaningful quartile analysis.

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Enter data and click Calculate to see quartile results.

What are Quartiles?

Quartiles divide an ordered dataset into four equal parts, each containing 25% of the data. They give a robust picture of spread and central tendency.

Five-Number Summary

Min — smallest value
Q1 — 25th percentile
Q2 — median (50th percentile)
Q3 — 75th percentile
Max — largest value

IQR Formula

IQR = Q3 − Q1

Measures the spread of the middle 50% of data. Outliers fall below Q1 − 1.5×IQR or above Q3 + 1.5×IQR.

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Understanding Quartiles & IQR

Exclusive vs Inclusive Method

The exclusive (Tukey) method excludes the median when splitting the lower and upper halves. This is the standard approach for Cambridge O Levels, A Levels, and IB Mathematics. The inclusive method includes the median value in both halves and is used in some FBISE and CBSE textbooks. When in doubt, check your syllabus or past paper mark schemes.

Using Quartiles in Exams

Quartile questions frequently appear in IGCSE, O Level, and A Level statistics papers. You may be asked to calculate Q1, Q2, Q3 from a list or frequency table, draw a box-and-whisker plot, compare two distributions using their IQR, or identify outliers using the 1.5×IQR rule. This tool shows every step exactly as expected in mark schemes.