4,994
edits
Changes
Jump to navigation
Jump to search
Line 21:
Line 21: + + + + + + + + + + +
→Other "measures of central tendency": A distribution in which 90% of the items are above average
**The [[harmonic mean]] is used when averaging speeds that are all measured along the same distance (rather than the same time).
**The [[harmonic mean]] is used when averaging speeds that are all measured along the same distance (rather than the same time).
**The [[root mean square]] is used in engineering power calculations, and heavily used in statistics in measurements of [[variance]].
**The [[root mean square]] is used in engineering power calculations, and heavily used in statistics in measurements of [[variance]].
==An example of average, median, and mode==
Consider the number of chapters in each of the thirty-nine books of the Old Testament.<ref>Chosen because it is an example of a set of numbers that is far from having a normal distribribution.</ref>. Ranked in order by number of chapters, the list is:
:1, 2, 3, 3, 3, 3, 4, 4, 4, 5, 7, 8, 9, 10, 10, 12, 12, 13, 14, 14, 21, 22, 24, 24, 25, 27, 29, 31, 31, 34, 36, 36, 40, 42, 48, 50, 52, 66, 150
*The thirty-nine books contain a total of 929 chapters, so the ''average'' number of chapters is 23.8.
*The middle item of the set is the twentieth item, with nineteen items below it and nineteen items above it; the twentieth item is 14, so the ''median'' number of chapters is 14.
*There are four books (Joel, Nahum, Habbakuk, and Zephaniah) that are 3 chapters long. The number 3 occurs more times in the list than any other. The ''mode'' of the set of numbers is 3.
The list contains many books with a small number of chapters, a few books with a large number of chapters, and one book (Psalms) with a much larger number of chapters than any of the others. This is an example of a "skewed distribution." In skewed distributions, the average and the median can be very different, as they are here.
Notice that 22 of the items have values below the average and only 17 have values above it. Thus, 56% of the items have values below the average.
On ''A Prairie Home Companion,'' Garrison Keillor jokes about Lake Wobegon where "all the children are above average." It is not actually possible for all of the items in a set to be "above average." However, it is easy to concoct a highly skewed distribution in which 90% of them are. Imagine a circus act with nine clowns and one macaque monkey, and ask "what is the average weight of the performers in the act?" If the clowns weigh about 150 pounds each and the monkey weighs about 10 pounds, then the average weight of the performers is 1360 pounds / 10 performers = 136 pounds. The monkey is below average, and the nine clowns—90% of the performers—are above average.
==The average as a "balance point"==
==The average as a "balance point"==