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Statistics
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Descriptive Statistics is the branch of statistics that concerns collecting data, analysing it and presenting the results graphically or via the calculation of statistical parameters, numbers used to describe a set of data. However, it is often not possible to obtain the value of a variable for every member in of population. In such a case data is collected from a sample, or a portion of the population, and used to infer information about the characteristics of the population as a whole. This is the situation to which the procedures described in this chapter are best suited.

On other occasions observations in Descriptive Statistics relate to the values observed when carrying out a random experiment. In such a case the objective of the sample results is to try to establish a theoretical model which governs the experiment.

In Statistics, WIRIS always works with decimal numbers, unlike other areas of knowledge. This is done in order to follow the norms of practice in this area.

Take a look at how a sample consisting of 3 zeros and 4 ones can be represented.

In the first case a List, which contains the elements of a sample, was considered, and in the second case, a Divisor was used to indicate how may times each value appears. Now let's look at some operations we can carry out with samples.

To finish the introduction, it should be noted that it is possible to group different samples of random variables using a Divisor. A detailed explanation of this functionality can be found in the Multisample description in the alphabetical index.

Before proceeding let's look at some examples to clarify what we mean:

In this section we explain the functions that WIRIS can apply to a data set (observations from a statistical variable), x={x1,x2,...,xn}.

mean:  command mean

where n=length(x).

geometric mean:  command geometric_mean

where n=length(x).

harmonic mean:  command harmonic_mean

where n=length(x).

variance:  command variance

Calculates the variance in accordance with the inferential definition. That is, where n=length(x),  mx=mean(x).

standard deviation:  command standard_deviation

where n=length(x), mx=mean(x).

median:  command median

If x1,x2,...,xn is an ordered sample, it is defined as

 xk if n=2k-1 (xk+xk+1)/2 if n=2k
where k is a whole number. If the sample is not ordered, it can simply be ordered and the definition above can then be applied.

quartile:  command quartile

Calculate the various quartiles of a sample. See the complete definition of the command quartile in the alphabetical index.

mode:  command mode

Calculates the most commonly occurring value in the sample. If there is more than one value occurring the maximum number of times, a list is returned with the various mode values.

WIRIS has various functions that accept samples with bivariate data as the argument, i.e. a sample of the following form (x1,y1),(x2,y2),...,(xn,yn). Notice from the examples below that, although data entry can be carried out independently for the first and second variables, it has to be assumed that they represent bivariate data.

All bivariate data commands accept a list of data points as an argument in place of two lists of numbers. In a perfectly natural way, WIRIS takes the abscissae of the points as the values of the first variable and the ordinates as the values of the second variable observed in the elements of the sample.

covariance:  command covariance

where mx=mean(x), my=mean(y).

correlation:  command correlation

This calculates Pearson's correlation coefficient for a set of bivariate data taken from a sample. This parameter indicates the degree of 'linear relationship' between one sample and another.

regression line:  command regression_line

Given a data sample (x1,y1),(x2,y2),...,(xn,yn), calculates the regression line determined using the least squares method, taking x as a predictor variable and y as a response variable.