A ranking is a relationship between a set of items such that, for any two items, the first is either 'ranked higher than', 'ranked lower than' or 'ranked equal to' the second. In mathematics, this is known as a weak order or total preorder of objects. It is not necessarily a total order of objects because two different objects can have the same ranking. The rankings themselves are totally ordered. For example, materials are totally preordered by hardness, while degrees of hardness are totally ordered.
By reducing detailed measures to a sequence of ordinal numbers, rankings make it possible to evaluate complex information according to certain criteria. Thus, for example, an Internet search engine may rank the pages it finds according to an estimation of their relevance, making it possible for the user quickly to select the pages they are likely to want to see.
Analysis of data obtained by ranking commonly requires non-parametric statistics.
Famous quotes containing the word ranked:
“The trumpets sound, the banners fly,
The glittering spears are ranked ready;
The shouts o war are heard afar,
The battle closes thick and bloody;
But its no the roar o sea or shore
Wad mak me langer wish to tarry;
Nor shout o war thats heard afar,
Its leaving thee, my bonnie Mary.”
—Robert Burns (17591796)
“When I think of him, and his six sons, and his son-in-law, not to enumerate the others, enlisted for this fight, proceeding coolly, reverently, humanely to work, for months if not years, sleeping and waking upon it, summering and wintering the thought, without expecting any reward but a good conscience, while almost all America stood ranked on the other side,I say again that it affects me as a sublime spectacle.”
—Henry David Thoreau (18171862)
“If to be venerated for benevolence, if to be admired for talents, if to be esteemed for patriotism, if to be beloved for philanthropy, can gratify the human mind, you must have the pleasing consolation to know that you have not lived in vain. And I flatter myself that it will not be ranked among the least grateful occurrences of your life to be assured that, so long as I retain my memory, you will be thought on with respect, veneration, and affection by your sincere friend.”
—George Washington (17321799)