A method of Gradation

Abstract

There are many methods to gradate a series of irregular values obtained by experiments or observations though most of tem are compound in process, the author's method developed here is very much simpler and more usable.
Let A_??_(X_??_) be a series of observed values and be expressed as continuous broken lines in a diagram in which the ordinate is A and the abscissa X. Further, let the middle Points of _??_, _??_, _??_, _??_ etc, B_??_, _??_, C_??_ etc, and _??_, _??_ be the coordinates of n, the middle 'point thus obtained then we have
_??_=x_n/2
_??_=1/2ⁿ{nC₀y₀+nC₁y₁+nC₂y₂+… +nC_ry_r+…+nC_ny_n}
where
nC_r=_??_ r=0.1.2.…n
_??_ may be considered as a weighted mean, the weights of which are given by the coefficients of binomial theorem.