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July 20

If you know the average of a group bigger or equalt to 2 ...

...you do not know anything about its elements (right?). Is there a name for this 'rule'? OsmanRF34 (talk) 17:54, 20 July 2012 (UTC)[reply]

Well, you might know some things. For example, if you have 2 elements and the average is 2.75, you know that at least one of the numbers isn't an integer. You also know at least one of the numbers is larger than or equal to the average and one is smaller or equal. So, for example, if the average is negative, at least one of the elements is negative. StuRat (talk) 18:53, 20 July 2012 (UTC)[reply]

"at least one of the numbers is larger than the average and one is smaller" -- being very pedantic, unless the numbers are equal... 86.179.1.131 (talk) 20:20, 20 July 2012 (UTC)[reply]

Fixed. StuRat (talk) 23:44, 20 July 2012 (UTC)[reply]

Such a rule wouldn't be too useful. First, you'll have to restrict it maybe to positive numbers like age, size, and so on. Second, if you do this, you end up with other additional information - you know that ages and sizes have a certain range. If I give you a group of 2 humans whose average is 2 meter, you can deduct that they are not very far away from 2 m each one. Third, in the same way that you obtained the average (from a series of measures), you can obtain other statistics - mean, mode, and all sorts of distribution patterns. 88.9.110.244 (talk) 23:35, 20 July 2012 (UTC)[reply]

If you just know that the average is at least 2 (but not what it is), there are some things you can say. Some element is greater than or equal to 2. If any element is less than 2, then some element is greater than 2. Maybe in a stretch you could say that these are the pigeonhole principle.

If you know the average precisely and that all the values are not negative, then you get Markov's inequality, which says that for any value x, at most a fraction of average/x elements have value greater than or equal to x. Rckrone (talk) 16:58, 21 July 2012 (UTC)[reply]