Median: Difference between revisions
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Any other lines which divide the area of the triangle into two equal parts do not pass through the centroid. |
Any other lines which divide the area of the triangle into two equal parts do not pass through the centroid. |
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==Median strip of a road== |
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On an [[expressway]], [[motorway]], or [[autobahn]], the '''median''' (called the '''central reservation''' in [[British English]]) is the strip of [[lawn|grass]] or the [[wall]] which separates opposing [[lane]]s of [[traffic]]. This is necessary because of [[safety]] concerns, due to the high speed of [[automobile]]s on both sides, and the potential [[danger]] of a disastrous head-on [[collision]] at the combined [[velocity|speed]] of both [[vehicle]]s. |
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Medians function secondarily as "green areas", beautifying [[road]]ways. Some [[jurisdiction]]s [[mow]] their medians, others scatter [[wildflower]] [[seed]]s which [[germinate]] and re-seed themselves every [[year]], while still others create extensive plantings of [[tree|trees]], [[shrub]]s, [[perennial plant|herbaceous perennials]] and decorative [[Poaceae|grasses]]. Where space is at a premium, dense [[hedge]]s of shrubs filter the headlights of oncoming traffic and provide a resilient barrier. |
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==See also== |
==See also== |
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Revision as of 00:32, 16 October 2004
- For the ancient Iranian people and country, see Medes.
In statistics, the median is that value that separates the highest half of the sample from the lowest half. More precisely 1/2 of the population will have values less than or equal to the median and 1/2 of the population will have values equal to or greater than the median. 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 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.
See also
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.