Five Number Summary & IQR Calculator
Last reviewed: July 2026 by the InvNorm Calculator Editorial Team. Report an issue
A five number summary (also called a 5 point summary) describes a data set using five values: the minimum, first quartile (Q1), median, third quartile (Q3), and maximum. Enter a list of numbers below to get the five number summary, the interquartile range (IQR), and any outliers, along with full step-by-step working.
What Is a Five Number Summary?
The five number summary is the standard way to describe the shape and spread of a data set with just five statistics. It is the foundation of a box plot (box-and-whisker plot), where the box spans Q1 to Q3, a line marks the median, and whiskers extend to the minimum and maximum (excluding outliers).
- Minimum: The smallest value in the data set.
- Q1 (first quartile): The median of the lower half of the data — 25% of values fall below Q1.
- Median (Q2): The middle value — 50% of values fall below the median.
- Q3 (third quartile): The median of the upper half of the data — 75% of values fall below Q3.
- Maximum: The largest value in the data set.
How to Find Q1 and Q3 (Median-of-Halves Method)
This calculator uses the median-of-halves method (also called Tukey's hinges), the method taught in most introductory statistics courses and used by the TI-84's 1-Var Stats function:
- Sort the data in ascending order.
- Find the median, splitting the data into a lower half and an upper half. If the data set has an odd number of values, the overall median is excluded from both halves.
- Q1 is the median of the lower half.
- Q3 is the median of the upper half.
Note: some software (including Excel's QUARTILE.INC and NumPy's default percentile) uses linear interpolation instead, which can give slightly different Q1/Q3 values for the same data set. Both methods are valid; the median-of-halves method matches what is taught alongside graphing calculators.
Interquartile Range (IQR) Explained
The interquartile range is the width of the middle 50% of the data:
IQR = Q3 − Q1
A five number summary and interquartile range calculator like this one is useful because IQR describes spread without being distorted by extreme values, unlike the range (max − min).
Identifying Outliers with the 1.5×IQR Rule
The most common rule for flagging outliers uses the IQR to build "fences" around the data:
- Lower fence = Q1 − 1.5 × IQR
- Upper fence = Q3 + 1.5 × IQR
Any value below the lower fence or above the upper fence is flagged as a statistical outlier. This calculator applies the 1.5×IQR rule automatically and lists any outliers found.
Worked Example
Data set: 3, 7, 8, 5, 12, 14, 21, 13, 18, 10, 45
- Sort: 3, 5, 7, 8, 10, 12, 13, 14, 18, 21, 45
- Median (n=11, odd): the 6th value = 12
- Lower half: 3, 5, 7, 8, 10 → Q1 = 7
- Upper half: 13, 14, 18, 21, 45 → Q3 = 18
- IQR: 18 − 7 = 11
- Fences: lower = 7 − 16.5 = −9.5, upper = 18 + 16.5 = 34.5
- Outliers: 45 is above the upper fence of 34.5, so it is flagged as an outlier.
Load this example in the calculator above.
Five Number Summary in Excel, Python, R, and TI-84
| Software | Q1 | Median | Q3 |
|---|---|---|---|
| Excel / Google Sheets | =QUARTILE.INC(range,1) | =MEDIAN(range) | =QUARTILE.INC(range,3) |
| Python (NumPy) | numpy.percentile(data, 25) | numpy.median(data) | numpy.percentile(data, 75) |
| R | quantile(data, 0.25) | median(data) | quantile(data, 0.75) |
| TI-84 / TI-83 | STAT → CALC → 1: 1-Var Stats (Q1 and Q3 shown in the output) | ||
Excel and NumPy use linear interpolation by default, so their Q1/Q3 values may differ slightly from the median-of-halves method used by this calculator and the TI-84.
Five Number Summary Calculator FAQs
A five number summary describes a data set using five values: the minimum, the first quartile (Q1), the median, the third quartile (Q3), and the maximum. Together these five numbers show the center, spread, and range of a data set without needing every individual value.
Yes. “5 point summary” and “five number summary” refer to the same set of statistics: minimum, Q1, median, Q3, and maximum. Both terms are used interchangeably in statistics courses and textbooks.
Sort the data, then find the median to split it into a lower half and an upper half. If the data set has an odd number of values, exclude the overall median from both halves. Q1 is the median of the lower half, and Q3 is the median of the upper half. This is called the median-of-halves method and is the same method used by the TI-84's 1-Var Stats function.
The interquartile range (IQR = Q3 − Q1) measures the spread of the middle 50% of a data set. It is used to describe variability in a way that is resistant to extreme values, and it forms the basis of the 1.5×IQR rule for identifying outliers.
Compute the IQR (Q3 − Q1), then calculate the lower fence as Q1 − 1.5×IQR and the upper fence as Q3 + 1.5×IQR. Any data point below the lower fence or above the upper fence is considered a statistical outlier.
Related Calculators
Z Score Calculator
Convert raw scores to Z scores and find probabilities.
Normal Distribution Calculator
Compute probabilities and values for any normal distribution.
InvNorm Calculator
Find X values and Z scores from normal probabilities.
Critical Value Calculator
Find critical values for confidence levels and hypothesis tests.
Return to the InvNorm Calculator to run your own calculation.