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    Re: Rejecting outliers: was: Kurtosis.
    From: Gary LaPook
    Date: 2011 Jan 1, 02:13 -0800

    Without getting into higher math(s) I agree with Peter's point that you will improve the average if you can identify data that has large errors prior to calculating that average. If you take a series of sights on the same body and you plot them versus a calculated slope, that the data should approximate, and you notice the last data point is not near the calculated slope, you investigate and find that your watch has stopped so the time of the last data point is suspect. I think anybody would then eliminate this data point even though watch stoppings are a form of random error. So how do you decide if a data point has such a large error that it should be eliminated prior to the averaging? I think a way to make this decision is to consider the normal Gaussian distribution. A navigator should have a good idea, based on his experience, what his sigma should be. He might have several, based on different observing conditions that he can apply in deciding which data points should be rejected. If you take a thousand sights you should expect 50 that exceed 2 sigmas and since this is part of a normal distribution you should not exclude these points in calculating an average. But if you only take five shots you should not expect any to exceed two sigmas (though it is possible though highly unlikely) if they are part of a normal distribution. So my take is that for a small number of shots you should exclude any that exceed two sigma since it is more likely that this is a result of some anomalous event and not part of a normal distribution that should be included in the average.

    gl
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