Quartile & IQR Calculator
Five-number summary: min, Q1, median, Q3, max and the IQR.
Median (Q2)
37.5
IQR = 19.5
Q1 (25%)
20.25
Q3 (75%)
39.75
IQR
19.5
Minimum
7
Maximum
41
Your sorted values. The median (Q2) is 37.5; the middle 50% of the data spans Q1 20.25 to Q3 39.75 (IQR 19.5).
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How the Quartile & IQR Calculator works
The Quartile & IQR Calculator computes the complete five-number summary — minimum, Q1, median, Q3, and maximum — along with the interquartile range (IQR) from any dataset you enter. It's built for students, researchers, analysts, and anyone who needs to quickly understand the spread and central tendency of numerical data without manual sorting or calculation.
To compute a five-number summary, the calculator first sorts your dataset in ascending order, then identifies five key positions: the smallest value (minimum), the largest value (maximum), and the three quartiles that divide the sorted data into four equal parts. The median (Q2) splits the dataset exactly in half, Q1 is the median of the lower half, and Q3 is the median of the upper half. This process gives you an immediate picture of where your data clusters, how it spreads, and whether it leans toward either extreme.
The interquartile range is calculated simply as IQR = Q3 − Q1, and it represents the middle 50% of your data. Unlike the full range (max − min), the IQR is resistant to outliers — a single extreme value won't inflate it. This makes it one of the most reliable single-number measures of statistical dispersion, especially for skewed distributions or real-world datasets that frequently contain anomalies like data entry errors or genuine extreme observations.
One important subtlety is that different software and textbooks use different methods for computing Q1 and Q3, particularly for small datasets or those with an even number of values. The most common approaches are the 'exclusive' method (used by many statistics textbooks, where the median itself is excluded from both halves before computing Q1 and Q3) and the 'inclusive' method (where the median is included in both halves). These methods can produce slightly different quartile values for the same dataset, so if your results need to match a specific course or tool like Excel or SPSS, confirm which convention is being used. Our calculator follows the standard exclusive (Tukey) method widely used in introductory statistics.
A common mistake is entering data in an unsorted or inconsistent format and assuming the first or last value represents the minimum or maximum — always let the calculator sort the data for you. Another frequent error is confusing the IQR with the standard deviation: the IQR is a range-based measure robust to outliers, while standard deviation is mean-based and sensitive to them. For heavily skewed data such as income distributions or test score distributions with a hard ceiling, the IQR and five-number summary are often more informative than mean and standard deviation alone.
Formula
IQR = Q3 − Q1
Pro tips
- Use the IQR to detect outliers automatically: any data point below Q1 − 1.5×IQR or above Q3 + 1.5×IQR by Tukey's rule is a candidate outlier worth investigating before drawing conclusions.
- When comparing two datasets, compare their IQRs side by side — a larger IQR means more variability in the middle of the distribution, which is often more meaningful than comparing full ranges that can be distorted by a single extreme value.
- For skewed distributions (such as household incomes, reaction times, or biological measurements), always report the median and IQR rather than mean and standard deviation — they give a more honest picture of where most values actually fall.
- If your quartile results don't match what Excel or your textbook shows, check which quartile method is being used: Excel's QUARTILE.EXC uses the exclusive method while QUARTILE.INC uses the inclusive method — these can differ noticeably for small samples.
- Always check your dataset size before interpreting Q1 and Q3: with very small samples (fewer than 8–10 values), quartiles become unreliable estimates of population quartiles, and conclusions about spread should be made cautiously.
Key terms
- Quartile
- — One of three values (Q1, Q2, Q3) that divide a sorted dataset into four equal parts, each containing 25% of the data.
- IQR (Interquartile Range)
- — The difference between the third quartile (Q3) and the first quartile (Q1), representing the spread of the middle 50% of a dataset.
- Five-Number Summary
- — A concise statistical description of a dataset consisting of the minimum, Q1, median, Q3, and maximum values.
- Median
- — The middle value of a sorted dataset (Q2), which divides the data into two equal halves and is resistant to the influence of outliers.
- Outlier
- — A data point that falls unusually far from the rest of the dataset, commonly defined as any value below Q1 − 1.5×IQR or above Q3 + 1.5×IQR using Tukey's fence rule.
- Box Plot (Box-and-Whisker Plot)
- — A graphical representation of the five-number summary that visually displays data spread, skewness, and potential outliers using a box spanning Q1 to Q3 with whiskers extending to the min and max.
