1、Designation: D 4375 96 (Reapproved 2006)Standard Practice forBasic Statistics in Committee D19 on Water1This standard is issued under the fixed designation D 4375; the number immediately following the designation indicates the year oforiginal adoption or, in the case of revision, the year of last re
2、vision. A number in parentheses indicates the year of last reapproval. Asuperscript epsilon (e) indicates an editorial change since the last revision or reapproval.1. Scope1.1 This practice establishes a uniform standard for calcu-lating, expressing, and symbolizing some basic statisticalparameters.
3、2. Referenced Documents2.1 ASTM Standards:2D 1129 Terminology Relating to WaterE 456 Terminology Relating to Quality and Statistics3. Terminology3.1 Definitions:3.1.1 populationthe set of data that consists of all possibleobservations or values of a certain phenomenon.3.1.2 samplea set of data from
4、the population.3.1.3 statistican estimated quantity for a parameter calcu-lated from a sample.3.1.4 parametera measurable quantity characteristic of apopulation.3.1.5 observationa fact duly noted and recorded.3.1.6 sample or population size(N may be finite orinfinite, but N and n are finite for all
5、calculations).3.1.7 For definitions of related statistical terms, see Termi-nology E 456.3.1.8 For definitions of other terms used in this practice,refer to Terminology D 1129.3.2 Symbols:Symbols for Sample and Population:SamplePopula-tionObservation xiXiSample or PopulationSizenNMean x Variance s2s
6、2Standard Deviation s sStandard Deviation of Mean sxsRelative Standard Deviation (%) RSD RSDp4. Summary of Practice4.1 Prior to performing many statistical procedures certainvariables need to be calculated. The technique for calculatingthese variables and presenting these results is developed in thi
7、spractice.5. Significance and Use5.1 This practice assures the user that all calculations areperformed in the same manner and that all results are presentedconsistently.6. Calculation of Statistical Parameters6.1 Mean:x 5(i 5 1nxi/n 5(i 5 1NXi/N6.2 Variance:s25(i 5 1nxi2 x!2/n21s25(i 5 1NXi2 !2/N6.3
8、 Standard Deviation:s 5 =s2s5=s26.4 Standard Deviation of the Mean(also known as stan-dard error of the mean):sx5 =s2/ns5 =s2/N6.5 Relative Standard Deviation (%)(also known as co-efficient of variation) expressed as a percentage:3RSD 5 100! s/x (1)1This practice is under the jurisdiction of ASTM Co
9、mmittee D19 on Water andis the direct responsibility of Subcommittee D19.02 on General Specifications,Technical Resources, and Statistical Methods.Current edition approved Aug. 15, 2006. Published August 2006. Originallyapproved in 1984. Last previous edition approved in 2001 as D 4375 96 (2001).2Fo
10、r referenced ASTM standards, visit the ASTM website, www.astm.org, orcontact ASTM Customer Service at serviceastm.org. For Annual Book of ASTMStandards volume information, refer to the standards Document Summary page onthe ASTM website.3Manual on Presentation of Data and Control Chart Analysis, 6th
11、Edition,ASTM MNL 7, ASTM, 1990, p. 19.1Copyright ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959, United States.RSDp5 100! s/7. Keywords7.1 notation; terminology; statisticsASTM International takes no position respecting the validity of any patent rights asse
12、rted in connection with any item mentionedin this standard. Users of this standard are expressly advised that determination of the validity of any such patent rights, and the riskof infringement of such rights, are entirely their own responsibility.This standard is subject to revision at any time by
13、 the responsible technical committee and must be reviewed every five years andif not revised, either reapproved or withdrawn. Your comments are invited either for revision of this standard or for additional standardsand should be addressed to ASTM International Headquarters. Your comments will recei
14、ve careful consideration at a meeting of theresponsible technical committee, which you may attend. If you feel that your comments have not received a fair hearing you shouldmake your views known to the ASTM Committee on Standards, at the address shown below.This standard is copyrighted by ASTM Inter
15、national, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959,United States. Individual reprints (single or multiple copies) of this standard may be obtained by contacting ASTM at the aboveaddress or at 610-832-9585 (phone), 610-832-9555 (fax), or serviceastm.org (e-mail); or through the ASTM website(www.astm.org).D 4375 96 (2006)2
