Stan Brown <[EMAIL PROTECTED]> wrote in news:[EMAIL PROTECTED]:
> The empirical rule tells you that _about_ 2.5% of the data will lie > above z = 2 in a normal distribution, not that _exactly_ 2.5% will > lie above. The smaller the population, the less closely it will > approach an ideal normal distribution and therefore the less good > that empirical rule will be. For 500 students the approximation > should not be too bad, _if_ the underlying distribution is > normal.(*) So your calculation correctly tells you that _about_ 12.5 > students will have scores over 83. You would simply state this as > about 12 or 13 students. Another way to put it is that the OP's original distribution is discrete, but he's approximating it with a continuous distribution, and the area under the appropriate part of the curve of a continuous distribution doesn't have to evenly divide that of a discrete one. > (*) I'm a little uneasy about that "mound shape distribution" in the > problem statement. I hope you understand, Mel, that the empirical > rule does not apply to every mound-shaped distribution but only to > normal distributions. Other mound-shaped distributions will differ > from the empirical rule to a greater or lesser extent. Same here. "Mound shaped" to me merely implies that the distribution is unimodal, in which the appropriate "empirical rule" is really the Camp- Meidel inequality; at most 1/(2.25*K^2) of the data will lie more than K standard deviations from the mean, regardless of the nature of the distribution (though even then it's an approximation when dealing with a discrete distribution). In the OP's case, that would be 11%. . . ================================================================= Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at: . http://jse.stat.ncsu.edu/ . =================================================================
