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A weighted arithmetic mean is obtained by multiplying each value by some non-negative weight before summation and then dividing the sum of the products by the sum of the weights.
Results of Astronomical and Meteorological Observations - Page xli

## A Treatise on Probability: Forming the Article Under that Head in the ...

Thomas Galloway - 1839 - 248 pages
...of the element is found by multiplying each observation by a number proportional to its weight, and dividing the sum of the products by the sum of the weights ; and the comparative weight of the result is unit divided by the sum of all the weights. If the weights...

## An Introduction to Natural Philosophy: Designed as a Text-book for the Use ...

Denison Olmsted - 1860 - 492 pages
...from that point is obtained by multiplying each weight into its own distance from the same point, and dividing the sum of the products by the sum of the weights. Let A, B, Fio. M. 0 ABCD i O °— i • <i G C, and D, represent the weights of several bodies, whose...

## Elements of the Method of Least Squares

Mansfield Merriman - 1877 - 220 pages
...probable value of the measured quantity is found by multiplying each observation ly its weight, and dividing the sum of the products by the sum of the weights. This value Z is called the General Mean to distinguish it from the arithmetical mean 20, which is only...

## Elementary Chemical Arithmetic: With 1100 Problems

Sydney Lupton - 1882 - 374 pages
...accuracy. The mean of the measured quantity is found by multiplying each observation by its weight, and dividing the sum of the products by the sum of the weights. The probable error of this general mean is *J9i +ffa+92+ &c- V n - 1 Thus the quantity of hydrogen...

## A Treatise on Practical Astronomy: As Applied to Geodesy and Navigation

Charles Leander Doolittle - 1883 - 666 pages
...value of the unknown quantity •will be obtained by multiplying each observation by its weight, and dividing the sum of the products by the sum of the weights. It is clear that the difference of weights may result from a variety of causes other than the simple...

## A Text Book on the Method of Least Squares

Mansfield Merriman - 1884 - 216 pages
...probable value of the unknown quantity z is obtained by multiplying each observation by its weight, and dividing the sum of the products by the sum of the weights. In order to distinguish this process from that of the arithmetical mean, it is sometimes called the...

H. C. Godwin - 1890 - 402 pages
...most probable value of the results will be found by multiplying each observed value by its weight, and dividing the sum of the products by the sum of the weights, the result being that value which renders the sum of the products of the squares of the errors and...

## An Introduction to Natural Philosophy: Designed as a Textbook in Physics for ...

Denison Olmsted - 1891 - 496 pages
...from that point is obtained by multiplying each weight into Us own distance from the same jtuitU, and dividing the sum of the products by the sum of the weights. Let A, B, C, and D, represent the weights of several bodies, whose centres of gravity are in the straight...