The Analyst Volume 9-10

The Analyst Volume 9-10

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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. 1882 edition. Excerpt: ...so that the common interval between them is reduced from Ax to Ax-t-k, their distribution along the X axis will represent the law of facility of error in the mean of k observations. The limits of possible error, which were kmAx for the sum, will be reduced to mAx for the mean, being the same as for a single observation. The centre of g. of all the masses I will now, as before, be the approximate place of the maximum, and its abscissa, or lever arm about the place of l0, will be reduced from kx1 to xlt showing that if there is any true error in the ultimate mean, or arith. mean of all the possible values, weighted for probabi'ty of occurrence, it is the same for the arith. mean of k observations, as it is for a single observation. Since the distance of each of the masses I from the centre of gravity is k times less for the arith. mean than it was for the sum, 1--k becomes a common coefficient of all the distances which go to make up the quadratic and cubic radii, which are consequently k times less for the mean than they were for the sum. Hence by (59), the q. m. error and c. m. inequality for the arith. mean of k observations will be e0 = e-V, Co = C+-. (60) When k is increased, the q. m. error of the mean diminishes, being inv'sely as j/&, T(while the c. m. inequality diminishes more rapidly, being inversely as fk. If we'take 64 times as many observations, the q. m. error of the mean result will be one eighth as large as before, but the c. m. inequality of the possible errors of the mean will be only one sixteenth as large as before. This goes to show that as k increases, the curve of facility of error in the mean, taken as a whole, becomes more and more symmetrical on either side of the centre of gravity. It may be...show more

Product details

  • Paperback | 98 pages
  • 189 x 246 x 5mm | 191g
  • Rarebooksclub.com
  • United States
  • English
  • black & white illustrations
  • 1236500946
  • 9781236500946