How to Find Median How to Find Median In the subject of the math the term median has got different types of the meanings in the different theories which are present. For example the term median has got one meaning in the theory of the geometry with respect to a triangle while it has got some different sense in the theory of the probability and in the theory of the statistics. So in this article we will discuss some of the important facts about the term median with respect to the both types of the theories which are mentioned above. So let us first start to discuss about the term median in the context of the theory of the geometry that is with respect to a triangle. In a triangle a median is a line segment which starts from one of the vertex of the triangle and ends on the opposite side of that vertex of that triangle and intersecting that opposite side at such a point which divides that side into two equal parts that is in short we can say that medians of the triangle bisect the sides of the triangle that is divide the sides of the triangle into two equal parts. There exist three medians in any triangle with respect to the three sides of the triangle. Now we have discussed about the role which the median plays in the theory of the geometry inside a triangle in the last paragraph so in this paragraph we will discuss about the meaning
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of the term median with reference to the theory of the probability and the theory of the statistics. In the context of the statistics and the theory of the probability, the term median is defined as a numerical value which separates half which is higher from the half which is lower, of any type of the sample or any population or any distribution of the probability. Now let us discuss about the method to find the median in the theory of the statistics or the theory of the probability. We can find the median of any such list of the numbers which is finite by rearranging every single observation from the value which is the smallest to the value which is the largest and then after that selecting the value which occurs in the middle position of that list of the numbers. It is very easy to find the median when there are odd numbers of the observations because then it is very simple to select the middle position of the rearranged list of the numbers. However when there exist an even number of the observations then we cannot find the median by just seeing the list and selecting the middle value because there does not exist any middle position in any list of an even number of the observations thus we have to calculate the median in such a condition by taking the mean of those two values which occur in the middle of the list. It should be noticed here that a median is defined just for data which is of single dimension while a geometric kind of the median can be defined for multi dimensions. In statistics and probability theory, median is described as the numerical value separating the higher half of a sample, a population, or a probability distribution, from the lower half. The median of a finite list of numbers can be found by arranging all the observations from lowest value to highest value and picking the middle one. If there is an even number of observations, then there is no single middle value; the median is then usually defined to be the mean of the two middle values.
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A median is only defined on one-dimensional data, and is independent of any distance metric. A geometric median, on the other hand, is defined in any number of dimensions. In a sample of data, or a finite population, there may be no member of the sample whose value is identical to the median (in the case of an even sample size), and, if there is such a member, there may be more than one so that the median may not uniquely identify a sample member. Nonetheless, the value of the median is uniquely determined with the usual definition. A related concept, in which the outcome is forced to correspond to a member of the sample, is the medoid. At most, half the population have values strictly less than the median, and, at most, half have values strictly greater than the median. If each group contains less than half the population, then some of the population is exactly equal to the median. For example, if a < b < c, then the median of the list {a, b, c} is b. If a <> b <> c as well, then only a is strictly less than the median, and only c is strictly greater than the median. Since each group is less than half (onethird, in fact), the leftover b is strictly equal to the median (a truism). Likewise, if a < b < c < d, then the median of the list {a, b, c, d} is the mean of b and c; i.e., it is (b + c)/2. The median can be used as a measure of location when a distribution is skewed, when end-values are not known, or when one requires reduced importance to be attached to outliers, e.g., because they may be measurement errors.
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