Statistics is the science of obtaining, synthesizing, predicting, and drawing inferences from data. Elementary calculations of mean and standard variation suffice to summarize a large, finite, normally-distributed dataset; the field of Statistics exists since data are not usually so nicely given. If we do not know all the elements of the dataset, we must discuss sampling and experimental design; if the data are not normal we must use other parameters to summarize them, or resort to nonparametric methods; if multiple data are involved, we study the measures of interaction among the variables. Other topics include the study of time-dependent data, and the foundations necessary to avoid ambiguity or paradox. Computational methods (e.g. for curve-fitting) are of particular importance in applications to the sciences and engineering as well as financial and actuarial work.
Certainly the greatest field of overlap with Statistics is 60: Probability.
For experimental design see also 05: Combinatorics.
Some questions on matching data to geometric figures are more properly a question of geometry (especially when there is a unique right answer).
For numerical methods, see 65U05. In particular, this applies to particular curve-fitting algorithms.
Clustering algorithms are related to nearest-neighbor methods in computational geometry.
Other fields with some overlap as seen in the diagram are areas 90 (Operations Research, Game Theory), 93 (Control Theory), 92 (Sciences), 65 (Numerical Analysis), 94 (Communication), 01 (History), 68 (Computer Science), 15 (Linear Algebra)
This image slightly hand-edited for clarity.
This is one of the largest areas in the Math Reviews database; many of the subfields listed above are fairly large. Indeed, the sub-areas 62G05 (nonparametric inference; estimation) and 62M10 (time series) are among the largest of the 5-digit areas.
Browse all (old) classifications for this area at the AMS.
Comprehensive: "Encyclopedia of statistical sciences", edited by Samuel Kotz, Norman L. Johnson and Campbell B. Read. John Wiley & Sons, Inc., New York, 1989. 6317pp in 9 volumes, plus supplements. MR90g:62001
Dated but useful: Kendall, Maurice G.; Doig, Alison G., "Bibliography of statistical literature" in 3 volumes: pre-1940, 1940--49, 1950--58. Oliver and Boyd, Edinburgh 1968 356 pp. MR41#2810
"A dictionary of statistical terms", first authored by M. G. Kendall and W. R. Buckland; fifth edition by F. H. C. Marriott: Longman Scientific & Technical, Harlow; copublished in the United States with John Wiley & Sons, Inc., New York, 1990. 223 pp. ISBN 0-582-01905-2 MR91j:62001
Sachs, Lothar: "A guide to statistical methods and to the pertinent literature", Springer-Verlag, Berlin-New York, 1986. 212 pp. ISBN 3-540-16835-4 MR88a:62001
Deely, J. J.: "What is Bayesian statistics?", New Zealand Oper. Res. 2 (1974), no. 2, 108--132. MR53#9440
Chen, Louis H. Y.: "What is nonparametric statistics?" Math. Medley 16 (1988), no. 2, 66--71. CMP992344
Roberts, Harry V.: "For what use are tests of hypotheses and tests of significance?", Comm. Statist.---Theory Methods A5 (1976), no. 8, 753--761. MR56#1549
Good, I. J.: "What is the use of a distribution?" Multivariate Analysis, II (Proc. Second Internat. Sympos., Dayton, Ohio, 1968) pp. 183--203; Academic Press, New York 1969 MR41#4703
Speed, T. P.: "What is an analysis of variance?", With a discussion and a reply by the author. Ann. Statist. 15 (1987), no. 3, 885--941. MR88k:62126
Ruppert, David: "What is kurtosis? An influence function approach", Amer. Statist. 41 (1987), no. 1, 1--5. CMP882763
Spitzer, John J.: "A primer on Box-Cox estimation", Rev. Econom. Statist. 64 (1982), no. 2, 307--313. MR83h:62055
Koopmans, L. H.: "A spectral analysis primer", Time series in the frequency domain, 169--183, Handbook of Statist., 3; North-Holland, Amsterdam, 1983. CMP749786
There are several statistics USENET newsgroups: sci.stat.math, sci.stat.edu, sci.stat.consult, comp.soft-sys.stat.spss, comp.soft-sys.stat.systat
An online text [Jan de Leeuw]
Another online text in statistics, this one with links to similar stat projects.
Introduction to Factor Analysis
Mailing lists: see http://www.stats.gla.ac.uk/allstat or http://www.mailbase.ac.uk/lists/minitab/files/list-of-lists
A full index to statistical routines and software is available at StatLib.
GAMS Statistics and Probability software.
A number of online calculators and other illustrative statistical tools.
Popular commercial statistical software includes SAS, SPSS, S-plus, etc.
Statlets: Java applets to perform the full range of elementary statistical analysis.
Packages for Mathematica, versions 2.2 and 3.0.