Median

Median givestechnical definitionmiddle innumbersenses.

Tablecontents

1 MedianStatistics 2 Median ofTriangle 3 Median strip ofroad

MedianStatistics

In statistics,medianthat value that separateshighest half ofsample fromlowest half. To findmedian, arrange allobservations from lowest valuehighest valuepickmiddle one. If therean even numberobservations, takemean oftwo middle values. When we usemediandescribe whatobservations havecommon, thereseveral choices formeasurevariability,range,interquartile range, andabsolute deviation. Sincemedian issame assecond quartile, its calculationillustrated inarticle on quartiles.

The medianprimarily usedskewed distributions, whichrepresents more accurately thanarithmetic mean. Considerset {1, 2, 2, 2, 3, 9}. The median2this case, as ismode,it might be seen asbetter indicationcentral tendency thanarithmetic mean3.166....

The medianalsocentral point which minimisesaverage ofabsolute deviations; inexample above this would be (1+0+0+0+1+7)/6=1.5 usingmedian, whilewould be 1.944... usingmean.

Even though sorting n items takesgeneral O(n log n) operations, by usingrecursive "Divide-and-Conquer" algorithmmediann items can be computedonly O(n) operations.

Calculationmedians ispopular techniquesummary statisticssummarizing statistical data, since itsimpleunderstandeasycalculate, while also givingmeasure thatmore robust inpresenceoutlier values than ismean. The difference betweenmedian andmeanless than or equalone standard deviation.

The medianalsocentral point which minimisessum ofabsolute average deviations.

Median ofTriangle

Intriangle,median isline joiningvertex tomidpoint ofopposite side. It dividestriangle into two partsequal area. The three medians intersect intriangle's centroid or centermass,two-thirds oflengtheach medianbetweenvertex andcentroid, while one-thirdbetweencentroid andmidpoint ofopposite side.

Any other lines which dividearea oftriangle into two equal parts do not pass throughcentroid.

Median strip ofroad

On an expressway, motorway, or autobahn,median isstripgrass orwall which separates opposing lanestraffic. Thisnecessary becausesafety concerns, due tohigh speedautomobiles on both sides, andpotential danger ofdisastrous head-on collision atcombined speedboth vehicles.

Medians function secondarily as "green areas", beautifying roadways. Some jurisdictions mow their medians, others scatter wildflower seeds which germinatere-seed themselves every year, while still others create extensive plantingstrees, shrubs, herbaceous perennialsdecorative grasses.