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Central Limit Theorem for Absolute Deviations from the Sample Mean and Applications
Canadian mathematical bulletin, Tome 22 (1979) no. 4, pp. 391-396

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The following type of argument is rendered almost believable by its frequent occurrence in elementary courses in statistics. Let ξi be a sequence of independent identically distributed random variables with means μ variances σ2. 
McLeish, D. L. Central Limit Theorem for Absolute Deviations from the Sample Mean and Applications. Canadian mathematical bulletin, Tome 22 (1979) no. 4, pp. 391-396. doi: 10.4153/CMB-1979-051-x
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     title = {Central {Limit} {Theorem} for {Absolute} {Deviations} from the {Sample} {Mean} and {Applications}},
     journal = {Canadian mathematical bulletin},
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     year = {1979},
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     doi = {10.4153/CMB-1979-051-x},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1979-051-x/}
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