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Discrete Variable

There are two main kinds of variables that we study in statistics : discrete and continuous. The discrete variables are defined as the variables having scores of a variable on the discrete scale. A discrete variable does not obtain on all values contained by the limits of the variable. Discrete variables explain a finite set of conditions and obtain values from a finite, typically small set of states. The fundamental property of variables is their domain. Variables that take on a finite number of values are called "discrete variables". We shall go ahead in this article and understand about discrete variables in detail.

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A discrete variable is one that cannot take on all values within the limits of the variable. It is a variables that can assign a finite number of values within it. All the qualitative variables are said to be discrete in nature. We may define a discrete variable as a type of statistical variable that is not continuous and it only takes on specific discrete values. It attains values which lie within a maximum and a minimum number.
Discrete variable is a quantitative variable that can assume a countable number of values.In other words, a discrete variable is a nominal or categorical variable having possible number of values to be finite. These values do not generally occur in some inherent order. For example - hair color and religion of a person would be two discrete variables, since it is quite evident that they both can contain only a limited values. Hair color may be brown, black, blonde, red etc and similarly religion may include Christian, Hindu, Judaism etc which do not have in any particular order.

Qualitative variables are discrete variables. Some quantitative variables are also discrete, such as the temperature counted to the nearest degree.Variables that are not discrete are called continuous.

Discrete Variable Example

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There are a number of examples in our daily life where the discrete variables are seen.

  1. Body temperature if categorized as as low, high and normal, would be discrete variable.
  2. If a coin is flipped to count the number of tails which could be any integer value within 0 and +infinity. However, it can take any number between 0 and infinity, it would not get 3.5 tails. Therefore, it is a discrete variable since the discrete variable cannot take on all the values within defined range.
  3. The number of siblings a person have, is a discrete variable because there would not be an infinite number of siblings, quite naturally. Also, it cannot be 1.5 siblings.
  4. Similarly, baby's age in months is a discrete variable.

Difference between Continuous & Discrete Variables

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The main difference between discrete variables and continuous variables is that the range of specified values is complete in discrete variables, whereas, in continuous, it is not a complete or whole value.

A discrete variable is one that can take on a countable number of different values, whereas a continuous variable is one that can take on an infinity number of the different values.

Discrete variables are the suitable approximation of real world quantities, sufficient for the function of reasoning. The success of a venture is represented by a continuous variable expressing the financial gain or stock price. It is also be discredited to Good, Better, Best.

For example, length of the stretched spring. Its length can be any value from its initial size to the maximum possible stretched size. The length variable can be 9.0 cm or 12.40 cm. The variation is continuous in nature.

Discrete Probability Distribution

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A discrete probability distribution defines the probability of the values of a discrete random variable. Every possible value of the discrete variable in discrete probability distribution is able to be related with a non-zero probability. So, the discrete probability distribution is generally illustrated in the form of a table. In short, the discrete probability distribution is defined as the table or graph of all possible values of a discrete random variable. There are many different types of discrete probability distributions. Few most important ones are listed below.
  1. Binomial probability distribution
  2. Poisson probability distribution
  3. Multinomial probability distribution
  4. Hypergeometric probability distribution
  5. Negative binomial distribution
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