woensdag 7 mei 2014

2.5.1. Range and Interquartile Range

The range is simply the largest value, minus the lowest value. Note that this is heavily influenced by extreme values and only compares two values in the data set. Since the range is easily influenced by extreme values, another approach might be to look at the difference between the third and first quartile, which is known as the interquartile range. The interquartile range still only looks at two values (1st and 3rd quartile) and ignores all other data points, but is not effected by extreme values.

History
One of the oldest references found to a range in statistics is from Lloyd (1848): "In choosing the particular hours for a continuous system of observations, we should select those which correspond nearly to the maxima and minima of the observed elements, so as to obtain also the daily range" (p. 182) Galton (1881) wrote: "This gave the upper and lower 'quartile' values, and consequently the 'interquartile' range..." (p. 245).

References 
Galton, F. (1881). Report of the Anthropometric Committee. Report of the British Association for the Advancement of Science, 51, 225–272. 
Lloyd, H. (1848). On Certain Questions Connected with the Reduction of Magnetical and Meteorological Observations. Proceedings of the Royal Irish Academy, 4, 180–183.

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