In mathematics and statistics, a quantitative variable may be continuous or discrete. If it can take on two real values and all the values between them, the variable is continuous in that interval. If it can take on a value such that there is a non-infinitesimal gap on each side of it containing no values that the variable can take on, then it is discrete around that value. In some contexts, a variable can be discrete in some ranges of the number line and continuous in others. In statistics, continuous and discrete variables are distinct statistical data types which are described with different probability distributions.
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👉 Discrete variable in the context of Bar chart
A bar chart or bar graph is a chart or graph that presents categorical data with rectangular bars with heights or lengths proportional to the values that they represent. The bars can be plotted vertically or horizontally. A vertical bar chart is sometimes called a column chart and has been identified as the prototype of charts.
A bar graph shows comparisons among discrete categories. One axis of the chart shows the specific categories being compared, and the other axis represents a measured value. Some bar graphs present bars clustered or stacked in groups of more than one, showing the values of more than one measured variable.
In this Dossier
- ⭐ Core Definition: Discrete variable
- 👉 Discrete variable in the context of Bar chart
- Discrete variable in the context of Discrete mathematics
- Discrete variable in the context of Digital signals
- Discrete variable in the context of Discrete optimization
- Discrete variable in the context of Optimization problem
Discrete variable in the context of Discrete mathematics
Discrete mathematics is the study of mathematical structures that can be considered "discrete" (in a way analogous to discrete variables, having a one-to-one correspondence (bijection) with natural numbers), rather than "continuous" (analogously to continuous functions). Objects studied in discrete mathematics include integers, graphs, and statements in logic. By contrast, discrete mathematics excludes topics in "continuous mathematics" such as real numbers, calculus or Euclidean geometry. Discrete objects can often be enumerated by integers; more formally, discrete mathematics has been characterized as the branch of mathematics dealing with countable sets (finite sets or sets with the same cardinality as the natural numbers). However, there is no exact definition of the term "discrete mathematics".
The set of objects studied in discrete mathematics can be finite or infinite. The term finite mathematics is sometimes applied to parts of the field of discrete mathematics that deal with finite sets, particularly those areas relevant to business.
View the full Wikipedia page for Discrete mathematicsDiscrete variable in the context of Digital signals
A digital signal is a signal that represents data as a sequence of discrete values; at any given time it can only take on, at most, one of a finite number of values. This contrasts with an analog signal, which represents continuous values; at any given time it represents a real number within an infinite set of values.
Simple digital signals represent information in discrete bands of levels. All levels within a band of values represent the same information state. In most digital circuits, the signal can have two possible valid values; this is called a binary signal or logic signal. They are represented by two voltage bands: one near a reference value (typically termed as ground or zero volts), and the other a value near the supply voltage. These correspond to the two values zero and one (or false and true) of the Boolean domain, so at any given time a binary signal represents one binary digit (bit). Because of this discretization, relatively small changes to the signal levels do not leave the discrete envelope, and as a result are ignored by signal state sensing circuitry. As a result, digital signals have noise immunity; electronic noise, provided it is not too great, will not affect digital circuits, whereas noise always degrades the operation of analog signals to some degree.
View the full Wikipedia page for Digital signalsDiscrete variable in the context of Discrete optimization
Discrete optimization is a branch of optimization in applied mathematics and computer science. As opposed to continuous optimization, some or all of the variables used in a discrete optimization problem are restricted to be discrete variables—that is, to assume only a discrete set of values, such as the integers.
View the full Wikipedia page for Discrete optimizationDiscrete variable in the context of Optimization problem
In mathematics, engineering, computer science and economics, an optimization problem is the problem of finding the best solution from all feasible solutions.
Optimization problems can be divided into two categories, depending on whether the variables are continuous or discrete:
View the full Wikipedia page for Optimization problem