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A correction which must be applied to the Moments computed from Normally Distributed data which have been binned. The corrected versions of the second, third, and fourth moments are
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(1) |
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(2) |
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(3) |
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(5) |
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(6) |
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(7) |
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(8) |
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(9) |
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(10) |
References
Kendall, M. G.; Stuart, A.; and Ord, J. K. Kendall's Advanced Theory of Statistics, Vol. 1: Distribution Theory, 6th ed.
New York: Oxford University Press, 1987.
Kenney, J. F. and Keeping, E. S. ``Sheppard's Correction.'' §4.12 in Mathematics of Statistics, Pt. 2, 2nd ed.
Princeton, NJ: Van Nostrand, pp. 80-82, 1951.