The median is the middle value when the data is arranged in order of size.
In other words, the median divides the whole set of values in two parts such that half of the observations are less than or equal to it and half are more than or equal to it.
If the total number of given values n, is an odd number, then there exists only one middlemost value, namely the th value in the arrangement and it represents the median of the values.
If the total number of given values n, is an even number, median may not be ubiquely determined. In fact, any possible value between the two middle values, namely, the th and the th values in the ordered arrangement, may be takes as median. But in order to obtain a definite value, the arithmetic mean of the th and the th values is regarded as the median of te set of values, by convention.
In relation to the frequency distribution of a continuous variable, the median is regarded as the value for which the cumulative frequency is . On observing the less-than type, say, cumulative frequencies, we can obtain the class interval that contains te median. In fact, the cumulative frequency for this interval is just more than or equal to . The value of the median can be approximately obtained by the following formula: (Proof):
or
where and c respectively represent the frequency and the width of the class-interval containing the median. Propiedades:
No le afectan las observaciones extremas.
Es fácil de calcular
Es siempre un valor de la variable.
La mediana divide el área total del histograma en dos iguales