The minimum and maximum are the two extremes of a data set. They tell you the full span of the data – the lowest and highest score, the coldest and warmest day, the shortest and longest ride – and they are the first and last entries of the five-number summary. Checking them is also the quickest way to catch data-entry errors: a negative age or a 1,000 km cycle commute stands out immediately.
Finding them by eye is easy for a short list but error-prone for long ones, especially with decimals. This calculator sorts the values, reports the minimum and maximum, and tells you at which position(s) in your original list they occur, which helps when the numbers come from a table and you need to find the matching row. If the extreme value appears more than once, every position is listed.
The second smallest and second largest values show whether an extreme is isolated (a large gap) or part of the main body of the data, and the range and midrange are given for convenience.
How to use the Min Max Calculator
- Data set
Everything is calculated in your browser, so results appear instantly and nothing you type is sent to a server.
How it works
Sort the values in ascending order; the first value is the minimum and the last is the maximum. Their positions are looked up in the list as you entered it.
Worked example
Eight bike rides in miles: 7.2, 3.9, 11.4, 5.6, 8.3, 3.9, 9.8, 6.1. Sorted: 3.9, 3.9, 5.6, 6.1, 7.2, 8.3, 9.8, 11.4. The minimum is 3.9 (rides 2 and 6) and the maximum is 11.4 (ride 3). The range is 7.5 miles and the midrange 7.65. The second largest ride, 9.8, is 1.6 miles below the maximum, so the longest ride is not wildly out of line.
Using the extremes
The minimum and maximum are the outer values of the five-number summary and the end points of the range. They are not robust – a single error changes them – so use them for data checking and for describing the span, and use quartiles or percentiles to describe typical low and high values.
Formula
Minimum = x₍₁₎ (first value after sorting) · Maximum = x₍ₙ₎ (last value) · Range = max − min
Worked example
Inputs — Data set: 7.2, 3.9, 11.4, 5.6, 8.3, 3.9, 9.8, 6.1.
Results — Minimum = 3.9; Maximum = 11.4; Position(s) of the minimum in your list = 2, 6; Position(s) of the maximum in your list = 3; Second smallest distinct value = 5.6; Second largest distinct value = 9.8.
Key terms
- Minimum
- The smallest value, x₍₁₎.
- Maximum
- The largest value, x₍ₙ₎.
- Range
- Maximum − minimum.
- Order statistic
- A value identified by its rank in the sorted data.
Frequently asked questions
How do I find the minimum and maximum of a data set?
Sort the values; the first is the minimum and the last is the maximum. For 7.2, 3.9, 11.4, 5.6, 8.3, 3.9, 9.8, 6.1 they are 3.9 and 11.4.
What if the minimum appears twice?
It is still one minimum value; the calculator lists both positions (2 and 6 in the example).
How do I find min and max in Excel?
=MIN(range) and =MAX(range); =SMALL(range, 2) and =LARGE(range, 2) give the second smallest and largest.
What is the range?
Maximum minus minimum: 11.4 − 3.9 = 7.5 in the example.
Is this the same as the minimum of a function?
No. This tool works on a list of numbers; finding the minimum of a function needs calculus or a graph.
Why check the min and max first?
Impossible extremes (negative weights, ages over 120) reveal data-entry errors before they distort the analysis.