what happens when a test company gets it wrong

10162014, 05:11 PM
(This post was last modified: 10162014 05:19 PM by Han.)
Post: #15




RE: what happens when a test company gets it wrong
(10132014 04:50 PM)Don Shepherd Wrote:(10122014 08:40 PM)Tim Wessman Wrote: but there are at least 3 ways to do it that I am aware of. All of them are mathematically and statistically valid. Here's one def. from wikipedia: "In statistics and probability theory, the median is the numerical value separating the higher half of a data sample, a population, or a probability distribution, from the lower half." If the sample is { 1, 5, 7, 9 } then ANY number strictly between 5 and 7 would satisfy this statement. The (most common) mathematical definition of median is: Quote:Given order statistics \( Y_1=min_j X_j, Y_2, ..., Y_{N1}, Y_N=max_j X_j, \) the statistical median of the random sample is defined by The problem with this definition is that it doesn't give a good intuitive explanation of median. For odd N we pick the "middle" term yet for even N we pick a number that isn't even in the list sample space. The definition of the term median determines whether the computed value of the median is "right" or "wrong." However, you insist that that mathematics does not allow for multiple interpretations (definitions, if you will) of a particular term. There are reasonable rationales for using the less typical definitions of median. If your domain is the set of integers, then a rational median may seem misplaced. Moreover, in the case of even elements, you are guaranteed that the median is within your set. I am not suggesting that these are the more common interpretations of median, but strictly speaking from a mathematical point of view, there is nothing wrong with "median" being interpreted differently. I do agree, however, that the more common interpretation should have been implemented. Joke: How does a mathematician catch a lion and place him into a cage? The mathematician goes into the cage, and defines "the inside" as the opposite side of where he is. Graph 3D  QPI  SolveSys 

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