Position measurements

Position measurements

1. This allows you to have the position of a value with respect to a set of data.

   • Maybe
     • Representative
     • Typical

2. Characteristics

   • Average
     • It is a value on the X scale corresponding to a frequency distribution, the value of which is calculated to represent it as a typical measure of the group.
       • Some essential conditions for this value to fulfill its mission:
         • It must be represented by a single figure.
         • It must be objective and defined by an algebraic formula, so that whoever person works with the distribution, the same value is always obtained.
         • It should be descriptive of the data, so that its meaning is easy to understand
   • Position or average measure
     • most used and understood by all, for its great stability is preferred in sampling, its formulas admit algebraic treatment. Its main disadvantage is to be very sensitive to changes in its values or observations, too, when any of its extreme values are too large or small.
       • Advantages
         • The arithmetic average is, in itself, the most understood and most used measure. It is such a value that if it were calculated for a group in which all the elements were equal, each of them would be equal to its arithmetic average, so we can deduce that the average of n elements, is a new element formed, corresponding to a part equal to 1 / n of each of the original elements.
         • This measure is defined by a mathematical equation very easy to understand and can sometimes be obtained when it is not possible to calculate other types of measures of central tendency or position and, even in cases where the individual values of the series are not known, for example: if 10 families consume 20 liters of milk, the arithmetic average will be 2 liters per family The arithmetic average is extraordinarily stable in sampling.
         • It is highly sensitive to any changes in distribution data.
         • As a final advantage, it can be noted that it is exceptionally adaptable when it comes to doing subsequent mathematical calculations with it.
       • Disadvantages
         • Is very sensitive to very small or large values, especially when these If the last ones are included in the distribution that is being studied, it can result in an average that does not represent the typical for the total of the group.
         • Where the distribution is markedly asymmetric, so that the arithmetic average, median and mode differ appreciably, consideration should always be given to the possibility that the arithmetic mean may not be the single representative value of the series.
         • Another drawback or disadvantage is when the distribution has the form of U, that is, parabolic: this corresponds to the less common values in the series and therefore, can give us an unreal idea of the distribution.
       • This measure, in general, is represented by an equis with a stripe or stroke placed on its top, however other symbols are used as can be seen below:
         • Reference: Martínez, E. (2020) Estadística. ed. Santiago de los Caballeros: Universidad Abierta para Adultos (UAPA). (pp 126-220). https://elibro-net.bibliotecavirtual.unad.edu.co/es/ereader/unad/175596/?page=22
   • Simple arithmetic mean

3. Central position measurements: indicate the central values of a distribution.

   • Mean: is the average of all data in the sample.
   • Median: is the mean value of all data sorted from lowest to highest.
   • Moda: es el valor que más se repite del conjunto de dato

4. Non-central position measurements: divide the dataset equally.

   • Cuartiles: dividen la muestra de datos en cuatro partes idénticas.
   • Quintiles: separate the data into five equal parts.
   • Deciles: split the dataset into ten intervals of the same amplitude.
   • Percentiles: divide the data into one hundred equivalent parts.

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