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Elements of Statistics Volume 2

Elements of Statistics Volume 2


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This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1920 Excerpt: ... nearly of the same magnitude as one of the individual errors, if these were not very unequal and all positive or all negative, and that if, as is generally the case, some are positive and some negative (a point we shall consider presently), the error would be considerably lessened; III. The error in a weighted, average is the sum of (1) an error due to errors in the quantities, similar to the error of an unweighted average, and (2) an error due to errors in the weights, which becomes very small when the original quantities are nearly equal. LetW, W, ... Wn be estimated weights applied to n estimated Error in quantities M1( M, ... Mn, and let the true values of weighted the weights be W, (i+-i). W, (i+ct)... and of the quantities be M, (i+e, ), M, ... Write Mw=-gTMr-, so that M is the estimated weighted average, and let Mb (i+e) be its true value. T, M v SW M (i+g) SWM Then M .E= sw (l+t) SW =SW.SW-M- (i+-) (i+e-)-SWM.SW( (i+-)-SW.SW (i+c), where the suffix t denotes any selected quantity, etc. Then--E.SWM.SW (i+c)=SW.SW, M, +SW.SW, M-SWM.SWw. Now suppose E, et, ft to be as small as 1, and neglect products which are as small as-oi. E. SWM. SW=SW. SW/M+SjW, (Mi. SW-SWM) -. SWJtftft SW, (Mt.SW-SWM) d SWM + SWM.SW The term involving et, the error in a quantity, is the same as that in Rule II., if W1M.l is written for mx, etc. The coefficient of et needs further analysis. Since SWM=M .SW, M-SW-SWM=SW. (M, -Mw)=m1, SW, where m1t is the excess of a quantity over the weighted average. swm-'swm Hence the resulting error due to the errors in quantities involves the magnitudes M1( Ms, etc., while that due to the errors in weights involves only the deviations of these quantities from their weighted a...


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Product Details
  • ISBN-13: 9781236213860
  • Publisher: Rarebooksclub.com
  • Publisher Imprint: Rarebooksclub.com
  • Height: 246 mm
  • No of Pages: 110
  • Spine Width: 6 mm
  • Width: 189 mm
  • ISBN-10: 1236213866
  • Publisher Date: 01 May 2012
  • Binding: Paperback
  • Language: English
  • Returnable: N
  • Weight: 213 gr


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