What Is Min Q1 Median Q3 Max?
The five-number summary describes a data set with five values: the minimum, the first quartile Q1, the median, the third quartile Q3 and the maximum. It is exactly what a box plot draws, and it gives a quick feel for centre, spread and skew without assuming a bell shape.
Paste your numbers and pick a quartile method. The textbook method takes the median of each half of the sorted data, while the Excel method interpolates between positions. The calculator returns the five numbers, the IQR, the range, the 1.5 × IQR fences, any outliers and a box plot.
Different books and programs define quartiles slightly differently, so if your answer differs from a key, change the method rather than assuming an error.
How to Use the Min Q1 Median Q3 Max Calculator
- Paste your data.
- Choose the quartile method your course or software uses.
- Read the five numbers and the outlier fences.
Min Q1 Median Q3 Max Formula
Interquartile range
Outlier fences
Min Q1 Median Q3 Max Variables Explained
| Symbol | Meaning | Notes |
|---|---|---|
| Q1 | First quartile, 25th percentile | |
| Median | Middle value, 50th percentile | |
| Q3 | Third quartile, 75th percentile | |
| IQR | Interquartile range, Q3 − Q1 | |
| Fences | Q1 − 1.5 IQR and Q3 + 1.5 IQR | Points beyond are outliers |
Min Q1 Median Q3 Max Worked Example
With the example values loaded in the calculator above, the steps are:
- Sort the data: 3, 5, 7, 8, 12, 13, 14, 18, 21.
- Minimum = 3, maximum = 21, median = 12.
- Quartiles by the exclusive median-of-halves method: Q1 = 6, Q3 = 16.
- IQR = 16 − 6 = 10; fences are -9 and 31.
Result: Minimum = 3; Q1 (first quartile) = 6; Median (Q2) = 12; Q3 (third quartile) = 16; Maximum = 21.
Worked example: 3, 5, 7, 8, 12, 13, 14, 18, 21
There are 9 values. The median is the 5th, which is 12. Excluding the median, the lower half is 3, 5, 7, 8 with median 6, and the upper half is 13, 14, 18, 21 with median 16.
So the summary is 3, 6, 12, 16, 21, with IQR = 10 and fences at −9 and 31. No value falls outside them.
Why quartile methods give different answers
There is no single agreed definition of a quartile. The textbook method splits the sorted data at the median, while Excel interpolates between positions. For some data sets the answers differ by a small amount. Pick the one your course uses.
Where Min Q1 Median Q3 Max Is Used
Drawing a box plot
Get the five numbers needed for a box and whisker plot.
Finding outliers
Flag values outside the 1.5 × IQR fences.
Describing skewed data
Summarise spread when the mean and standard deviation mislead.
Common Min Q1 Median Q3 Max Mistakes to Avoid
- Sort the data before finding quartiles by hand.
- Use the IQR rather than the range when outliers are present.
Min Q1 Median Q3 Max Terms and Definitions
- Quartile
- A value that splits sorted data into four parts with equal counts.
Min Q1 Median Q3 Max FAQs
What is the five-number summary?
The minimum, Q1, median, Q3 and maximum of a data set.
How do you find Q1 and Q3?
Sort the data, find the median, then take the median of the lower half for Q1 and of the upper half for Q3.
What is the IQR used for?
It measures the spread of the middle 50% of the data and is used to flag outliers.
How do I find outliers?
Values below Q1 − 1.5 × IQR or above Q3 + 1.5 × IQR are flagged as outliers.
Why does my answer differ from Excel?
Excel uses linear interpolation. Choose that method here to match QUARTILE.INC.
How many values do I need?
At least 4 for this calculator, but the summary is more meaningful with more data.