The Freedmen's Savings Bank

Bibliographic data

Monograph

Identifikator:: 175265076X

URN:: urn:nbn:de:zbw-retromon-129631

Document type:: Monograph

Author:: Fleming, Walter Lynwood http://d-nb.info/gnd/120660560X

Title:: The Freedmen's Savings Bank

Place of publication:: Chapel Hill

Publisher:: Univ. of North Carolina Press

Year of publication:: 1927

Scope:: x, 170 S.

Digitisation:: 2021

Collection:: Economics Books

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XVIL.—SIMPLER CASES OF SAMPLING FOR VARIABLES. 339 “peaked” distribution by superposing a normal curve with a small standard-deviation on a normal curve with the same mean and a relatively large standard-deviation. To give some idea of the reduction in the standard error of the median that may be effected by a moderate change in the form of the distribution, let us find for what ratio of the standard-deviations of two such curves, having the same area, the standard error of the median reduces to o//n, where o is of course the standard-deviation of the com- pound distribution. Let oy, 0, be the standard-deviations of the two distributions, and let there be n/2 observations in each. Then of +o} g= v “5 (@) On the other hand, the value of Y, 18— IRE Mgr 1 Wo 22x. 0 22.0, 2 Hence the standard error of the median is / 2r S199 [AY Von oy, + oy (¢) is equal to o/In if (01+ 03) Voitai_, 2 roe, : Writing oy/o =p, that is if (Lp) JT+p2_, 2 Amp P +203 + (2 - 4m)p2 + 2p +1 =0. This equation may be reduced to a quadratic and solved by 1 taking p + 28 & new variable. The roots found give p=2-2360 +v..0r 04472... the one root being merely the reciprocal of the other. The standard error of the median will therefore be /y/n, in such a compound distribution, if the standard-deviation of the one normal curve is, in round numbers, about 2} times that of the other. If the ratio be greater, the standard error of the median will be less than a/n/n. The distribution or (e, \S,

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