[ SOU ] 
IX. On the Mathematical Foundations of Theoretical Statistics. 
By 11. A. Fisher, M.A., Bellow of Gonville and Caius College, Cambridge, Chief 
Statistician, Rothamsted Experimental Station, Harpenden. 
Communicated by Dr. E. J. Russell, F.R.S. 
Received June 25,—Read November 17, 1921. 
Contents. 
Section Page 
1. The Neglect of Theoretical Statistics.310 
2. The Purpose of Statistical Methods.311 
3. The Problems of Statistics.313 
4. Criteria of Estimation. 316 
5. Examples of the Use of Criterion of Consistency.317 
6. Formal Solution of Problems of Estimation.323 
7. Satisfaction of the Criterion of Sufficiency. 330 
8. The Efficiency of the Method of Moments in Fitting Curves of the Pearsonian Type III . . 332 
9. Location and Scaling of Frequency Curves in general.338 
10. The Efficiency of the Method of Moments in Fitting Pearsonian Curves.342 
11. The Reason for the Efficiency of the Method of Moments in a Small Region surrounding the 
Normal Curve. 355 
12. Discontinuous Distributions.356 
(1) The Poisson Series . 359 
(2) Grouped Normal Data.359 
(3) Distribution of Observations in a Dilution Series.363 
13. Summary.366 
Definitions. 
Centre of Location. —That abscissa of a frequency curve for which the sampling errors 
of optimum location are uncorrelatecl with those of optimum scaling. (9.) 
Consistency. —A statistic satisfies the criterion of consistency, if, when it is calculated 
from the whole population, it is equal to the required parameter. (4.) 
Distribution. —Problems of distribution are those in which it is required to calculate 
the distribution of one, or the simultaneous distribution of a number, of functions of 
quantities distributed in a known manner. (3.) 
Efficiency. —The efficiency of a statistic is the ratio (usually expressed as a percentage) 
which its intrinsic accuracy bears to that of the most efficient statistic possible. It 
VOL. CCXXII.- -A 602. 2 X [Published April 19, 1922. 
