The Five Number Summary Calculator returns the minimum, first quartile (Q1), median, third quartile (Q3) and maximum of any pasted data set, the five values that describe both the center and the spread of a distribution without needing squared units. Paste values separated by commas, spaces or line breaks, choose a quartile method, and the tool returns all five figures with the sorted list shown alongside.
The five-number summary is the foundation of a box plot and a compact way to describe a data set's shape at a glance: how wide the whole range is, where the middle half sits, and whether the data leans toward one end.
Find the five-number summary
The five-number summary lists, in order: the minimum, the first quartile, the median, the third quartile, and the maximum.
Worked example: the data set 6, 7, 15, 36, 39, 40, 41 (already sorted, using the exclusive quartile method). Minimum: 6, the smallest value. Q1: 7, the median of the lower half (excluding the overall median). Median (Q2): 36, the middle value of the full sorted set. Q3: 40, the median of the upper half (excluding the overall median). Maximum: 41, the largest value.
Those five numbers alone reveal a long lower stretch (6 up to 36) and a tight upper cluster (36 to 41), a shape that would be much harder to see from the mean and standard deviation alone.
Calculate the interquartile range
The interquartile range (IQR) is Q3 minus Q1, and it measures the width of the middle 50 percent of the data, ignoring the tails entirely.
IQR = Q3 − Q1Worked example: using the same data set, Q3 = 40 and Q1 = 7.
IQR = 40 − 7 = 33.
Because IQR ignores the extreme tails, a single very high or very low outlier cannot inflate it the way it inflates the full range (maximum minus minimum), which for this same set is 41 − 6 = 35, only slightly larger than the IQR here since the tails in this particular set are short.
Choose a quartile method
Different textbooks and software packages calculate Q1 and Q3 slightly differently, particularly for small data sets, so naming the method used matters for matching a specific answer key.
| Method | Behavior | Familiar from |
|---|---|---|
| Exclusive (default) | Median excluded from both halves | Excel QUARTILE.EXC, many US textbooks |
| Inclusive | Median included in both halves when n is odd | Excel QUARTILE.INC, many TI calculators |
| Linear interpolation | Fractional position with interpolation | R type 7, NumPy default |
| Nearest rank | Returns an observed value, no interpolation | Some introductory courses |
Confirming which method a course or software package expects, before comparing an answer, avoids a mismatch that looks like an arithmetic error but is really just a difference in convention.
Use the five-number summary for outlier detection
A common rule flags a value as a potential outlier if it falls more than 1.5 times the IQR below Q1 or above Q3.
lower fence = Q1 − 1.5 × IQR
upper fence = Q3 + 1.5 × IQRWorked example: using Q1 = 7, Q3 = 40, and IQR = 33.
Lower fence: 7 − (1.5 × 33) = 7 − 49.5 = −42.5. Upper fence: 40 + (1.5 × 33) = 40 + 49.5 = 89.5.
Since the minimum (6) and maximum (41) in this set both fall within those fences, none of the values would be flagged as an outlier under this rule, despite the set's uneven spread.
Draw a box plot from the five-number summary
The five-number summary is exactly what a box plot needs: a box drawn from Q1 to Q3 with a line at the median, and whiskers extending out to the minimum and maximum (or to the outlier fences, with points beyond plotted separately, in some variants).
This makes the five-number summary a natural bridge between a numeric summary and a visual one.
Compare fence width to the actual range
For this data set, the fence width (upper fence minus lower fence) spans 89.5 − (−42.5) = 132, far wider than the actual range of 35. That gap shows the 1.5×IQR rule is deliberately generous for a small, tightly clustered upper group like this one, rarely flagging a value unless it sits well outside the observed spread.
Frequently asked questions
What is the five-number summary?
The minimum, first quartile (Q1), median, third quartile (Q3), and maximum of a data set, in that order. Together they describe both the center and the spread of the distribution.
How do you calculate Q1 and Q3?
Sort the data, then find the median of the lower half for Q1 and the median of the upper half for Q3, though the exact handling of the overall median in each half varies by method (exclusive, inclusive, interpolation, or nearest rank).
What is the interquartile range?
IQR = Q3 − Q1, the width of the middle 50 percent of the sorted data. It ignores the tails, making it resistant to distortion from a single extreme value.
How do you detect outliers using the five-number summary?
A common rule flags any value below Q1 − 1.5×IQR or above Q3 + 1.5×IQR as a potential outlier.
Why do different tools give different Q1 and Q3 values for the same data?
Because at least four different methods exist for calculating quartiles, and they can disagree, particularly on small data sets. Checking which method a specific tool or textbook uses resolves most discrepancies.
What is the five-number summary used for?
It is the basis of a box plot and a compact way to describe a distribution's center and spread without needing squared units like variance, which keeps every figure in the original measurement scale.
Does the five-number summary tell you about outliers directly?
Not by itself, but combined with the 1.5×IQR fence rule, it provides a standard method for flagging values that fall unusually far from the bulk of the data.
Summary
The five-number summary, minimum, Q1, median, Q3 and maximum, describes a data set's shape compactly, such as 6, 7, 36, 40, 41 for the set 6, 7, 15, 36, 39, 40, 41, revealing a long lower stretch and a tight upper cluster.
The interquartile range, Q3 minus Q1, measures the spread of the middle half and feeds directly into the standard 1.5×IQR rule for flagging potential outliers.