Univariate measures

Univariate measures

1. In statistics, the function through which a qualitative analysis of the corresponding graph is carried out is called a statistician; that is to say: the characterization of the set through the form of its distribution.

   • All the same
     • it is possible to obtain certain numerical quantities that allow a greater characterization of the set. Numerical Characteristics Arising from the Particular Values x1, x2, x3 … xn, in other words, are functions of these values.

2. There are four types of statisticians: position statisticians, dispersion statisticians, pointing statisticians, and deformation statisticians.

   • Position statisticians
     • are divided into two types:
       • -Statisticians of central tendency: provide information about the center of the distribution
         • Median
           • That value that is not exceeded or exceeds more than half of the observations in the set. In the calculation of the median, two situations must be distinguished depending on whether the number of observations is odd or even. If n is odd, it is enough to order the observations x(1) x(2) …, x(n) and take the central value as the median value, that is, x(n+1)/2. This is valid for both continuous variables and discrete variables. If n is even, after ordering the sample there are two central values, and any of them, or any between them, can be taken as the median. Consequently, with the definition of the median, it is easy to see that it represents the central value of the set of observations.
           • The median is that value that is precisely in the center of the set of observations, and with this it indicates that before and after it there are no more than half of the observations.
         • Medium
           • The arithmetic mean (or arithmetic mean) of a set x1, …., xn, of n values of a variable X is defined as:
           • The arithmetic mean is the balance point of the set of values.
       • -Location statisticians: indicate the location of extreme values or more frequent values.
         • Mode
           • The mode is the set of n values x1, x2, …, xn of the variable X, it is defined as the most frequent value, that is, the value that has the property of having a higher frequency (absolute or relative). This may or may not exist, there may even be more than one mode in the same set: we will denote this as Mo (x).
           • When there is only one mode, the distribution is said to be unimodal, when there are two, bimodal, and when there are three or more, multimodal.

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