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Median

Median gives a technical definition of middle is a number of senses.

Median in Statistics

In statistics, the median is that value that separates the highest half of the sample from the lowest half. To find the median, arrange all the observations from lowest value to highest value and pick the middle one. If there are an even number of observations, take the mean of the two middle values. When we use the median to describe what the observations have in common, there are several choices for a measure of variability, the range, the interquartile range, and the absolute deviation. Since the median is the same as the second quartile, its calculation is illustrated in the article on quartiles.

The median is primarily used for skewed distributions, which it represents more accurately than the arithmetic mean. Consider the set {1, 2, 2, 2, 3, 9}. The median is 2 in this case, as is the mode, and it might be seen as a better indication of central tendency than the arithmetic mean of 3.166....

The median is also the central point which which minimises the average of the absolute deviations; in the example above this would be (1+0+0+0+1+7)/6=1.5 using the median, while it would be 1.944... using the mean.

Even though sorting n items takes in general O(n log n) operations, by using a recursive "Divide-and-Conquer" algorithm the median of n items can be computed with only O(n) operations.

Calculation of medians is a popular technique in summary statistics and summarizing statistical data, since it is simple to understand and easy to calculate, while also giving a measure that is more robust in the presence of outlier values than is the mean. The difference between the median and the mean is less than or equal to one standard deviation.

The median is also the central point which which minimises the sum of the absolute average deviations.

Median of a Triangle

In a triangle, a median is a line joining a vertex to the midpoint of the opposite side. It divides the triangle into two parts of equal area. The three medians intersect in the triangle's centroid or center of mass, and two-thirds of the length of each median is between the vertex and the centroid, while one-third is between the centroid and the midpoint of the opposite side.

Any other lines which divide the area of the triangle into two equal parts do not pass through the centroid.