ASTM D4375-96(2006)

NOTICE: This standard has either been superseded and replaced by a new version or withdrawn.
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Designation:D4375–96 (Reapproved 2006)
Standard Practice for
Basic Statistics in Committee D19 on Water
This standard is issued under the fixed designation D4375; the number immediately following the designation indicates the year of
original adoption or, in the case of revision, the year of last revision. A number in parentheses indicates the year of last reapproval. A
superscript epsilon (´) indicates an editorial change since the last revision or reapproval.
1. Scope
Relative Standard Deviation (%) RSD RSD
p
1.1 This practice establishes a uniform standard for calcu-
4. Summary of Practice
lating, expressing, and symbolizing some basic statistical
4.1 Prior to performing many statistical procedures certain
parameters.
variables need to be calculated. The technique for calculating
these variables and presenting these results is developed in this
2. Referenced Documents
2 practice.
2.1 ASTM Standards:
D1129 Terminology Relating to Water
5. Significance and Use
E456 Terminology Relating to Quality and Statistics
5.1 This practice assures the user that all calculations are
performed in the same manner and that all results are presented
3. Terminology
consistently.
3.1 Definitions:
3.1.1 population—thesetofdatathatconsistsofallpossible
6. Calculation of Statistical Parameters
observations or values of a certain phenomenon.
6.1 Mean:
3.1.2 sample—a set of data from the population.
3.1.3 statistic—an estimated quantity for a parameter calcu-
n
lated from a sample.
x¯ 5 x /n
(
i
3.1.4 parameter—a measurable quantity characteristic of a
i 5 1
population.
N
3.1.5 observation—a fact duly noted and recorded. µ 5 X /N
( i
i 5 1
3.1.6 sample or population size—(N may be finite or
6.2 Variance:
infinite, but N and n are finite for all calculations).
n
3.1.7 For definitions of related statistical terms, see Termi-
2 2
s 5 ~x 2 x¯! /n21
(
i
nology E456.
i 5 1
3.1.8 For definitions of other terms used in this practice,
N
2 2
refer to Terminology D1129. s 5 ~X 2 µ! /N
(
i
i 5 1
3.2 Symbols:Symbols for Sample and Population:
6.3 Standard Deviation:
Popula-
Sample
tion
s 5 =s
Observation x X
i i
Sample or Population nN
s5 s
=
Size
Mean x¯ µ
6.4 Standard Deviation of the Mean—(also known as stan-
2 2
Variance s s
dard error of the mean):
Standard Deviation s s
Standard Deviation of Mean s s
x¯ µ
s 5 =s /n
x¯
s 5 s /N
=
µ
...