CORRECTION: Re: [math-fun] Sex, Lies and Government Conducted Surveys
CORRECTIONS: I stupidly rushed the "asimov median" post into print with a number of errors. Here is the corrected definition -- sorry. Correct definition: ------------------------------------------------------------------------------------------------ Assume the data sorted by size: x(1) <= x(2) <= . . . <= x(N). Let J be the smallest [interval of indices] that is symmetrical about the real number (N+1)/2, such that J contains a) all repetitions of x((N+1)/2) if N is odd, or b) all repetitions of both data x(N/2) and x(N/2 + 1) if N is even. Now define the "asimov median" as the average of all values whose indices lie in J. Thus if N = 200 and the sorted data looks like this: sort #: . . . 94 95 96 97 98 99 100 101 102 103 104 105 106 . . . datum: . . . 2 3 3 3 4 4 4 4 4 4 4 4 5 . . . then one may wish to say the asimov median is the average of data whose indices k satisfy 100.5 - 5 <= k <= 100.5 + 5, i.e., 96 <= k <= 105, so we get a.m. = (3+3+4+4+4+4+4+4+4+4)/10 = 3.8 . --Dan
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