This is an entry-level discussion of an advanced topic. For more comprehensive and rigorous treatment, see minima and maxima or extreme value.

The minimum of a set of numbers is the smallest value in that set. So, for the set of numbers {3, 7, 11, 30, 68, 121} the minimum is 3. The maximum of a set is the largest value it that set; for the set above, the maximum is 121.

In common usage, the terms "minimum" and "maximum" are used to communicate restrictions. For example, if a sale item is marked "maximum 3 per customer", it is restricting the number a single shopper may purchase. Similarly, a fairground ride with a sign saying "you must be this tall to ride" is giving a minimum size limit on who can ride safely.

Minimum and maximum values are also used in descriptive statistics

Descriptive statistics

Descriptive statistics quantitatively describe the main features of a collection of data. Descriptive statistics are distinguished from inferential statistics , in that descriptive statistics aim to summarize a data set, rather than use the data to learn about the population that the data are...

—along with the mean

Mean

In statistics, mean has two related meanings:* the arithmetic mean .* the expected value of a random variable, which is also called the population mean....

, median

Median

In probability theory and statistics, a median is described as the numerical value separating the higher half of a sample, a population, or a probability distribution, from the lower half. The median of a finite list of numbers can be found by arranging all the observations from lowest value to...

, and standard deviation

Standard deviation

Standard deviation is a widely used measure of variability or diversity used in statistics and probability theory. It shows how much variation or "dispersion" there is from the average...

—to provide a clear overview of a set of measurements without needing to quote the entire set. For example, consider the following two sets of numbers: set A, which is all the numbers from 0 to 100; and set B, which is a set of the number 50, 101 times. Both of these sets have an average

Average

In mathematics, an average, or central tendency of a data set is a measure of the "middle" value of the data set. Average is one form of central tendency. Not all central tendencies should be considered definitions of average....

 of 50, so from that statistic

Statistic

A statistic is a single measure of some attribute of a sample . It is calculated by applying a function to the values of the items comprising the sample which are known together as a set of data.More formally, statistical theory defines a statistic as a function of a sample where the function...

 alone, they appear identical. When the minima and maxima of the two sets are given as well, the difference becomes clear: for set A, the minimum is 0 and the maximum is 100, while for set B, both the minimum and maximum are 50.

The concept of minima and maxima also occurs in line graph

Graph of a function

In mathematics, the graph of a function f is the collection of all ordered pairs . In particular, if x is a real number, graph means the graphical representation of this collection, in the form of a curve on a Cartesian plane, together with Cartesian axes, etc. Graphing on a Cartesian plane is...

s, where the minimum is the lowest point of the line and the maximum is the highest. If a point is the lowest everywhere on the line, it is called the global minimum; if it's only the lowest in a specific area, for example the lowest point of a dip in the line, it's called a local minimum. The mathematical field of calculus

Calculus

Calculus is a branch of mathematics focused on limits, functions, derivatives, integrals, and infinite series. This subject constitutes a major part of modern mathematics education. It has two major branches, differential calculus and integral calculus, which are related by the fundamental theorem...

 investigates methods for finding both minima and maxima of any function

Function (mathematics)

In mathematics, a function associates one quantity, the argument of the function, also known as the input, with another quantity, the value of the function, also known as the output. A function assigns exactly one output to each input. The argument and the value may be real numbers, but they can...

.