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In contrast, a variable is a discrete variable if and only if there exists a one-to-one correspondence between this variable and a subset of , the set of natural numbers. [8] In other words, a discrete variable over a particular interval of real values is one for which, for any value in the range that the variable is permitted to take on, there ...
Common examples of measures of statistical dispersion are the variance, standard deviation, and interquartile range. For instance, when the variance of data in a set is large, the data is widely scattered. On the other hand, when the variance is small, the data in the set is clustered.
Because variables conforming only to nominal or ordinal measurements cannot be reasonably measured numerically, sometimes they are grouped together as categorical variables, whereas ratio and interval measurements are grouped together as quantitative variables, which can be either discrete or continuous, due to their numerical nature.
In statistics, the mode is the value that appears most often in a set of data values. [1] If X is a discrete random variable, the mode is the value x at which the probability mass function takes its maximum value (i.e., x=argmax x i P(X = x i)).
Data (/ ˈ d eɪ t ə / DAY-tə, US also / ˈ d æ t ə / DAT-ə) are a collection of discrete or continuous values that convey information, describing the quantity, quality, fact, statistics, other basic units of meaning, or simply sequences of symbols that may be further interpreted formally. A datum is an individual value in a collection of ...
Discrete probability distribution: for many random variables with finitely or countably infinitely many values. Probability mass function (pmf): function that gives the probability that a discrete random variable is equal to some value. Frequency distribution: a table that displays the frequency of various outcomes in a sample.
The standard deviation of a probability distribution is the same as that of a random variable having that distribution. Not all random variables have a standard deviation. If the distribution has fat tails going out to infinity, the standard deviation might not exist, because the integral might not converge.
A discrete variable that can take only one state contains zero information, and 2 is the next natural number after 1. That is why the bit, a variable with only two possible values, is a standard primary unit of information. A collection of n bits may have 2 n states: see binary number for details.