Atlas Copco ACTA 3000

ACTA 4000 User Guide Printouts from ACTA
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9.1 Principal definitions
Table 1 shows the following parameters that define a normal distribution:
Symbol Meaning
x
i
Individual measurement (lower case x)
n Number of individual measurements in a group
i Index digit of a group
X
X-bar
Mean value for a group (upper case X)
x
σ
Standard deviation (average uncertainty) in a series of x
X
σ
Standard deviation of a group mean an X-bar
Table 1 Normal distribution parameters
The arithmetical mean value of a group of individual measurements x
1
, x
2
, x
3
, …, x
n
is hereafter referred
to as group mean or X-bar and is defined by Equation 1:
n
x...xxx
X
n
++++
=
321
Equation 1 X-bar
The geometrical mean (always a positive number) of individual deviations from a group average is given
by the standard deviation for that group. It is defined by Equation 2:
()()()
(
)
1
22
3
2
2
2
1
−
−++−+−+−
=σ
n
Xx....XxXxXx
n
x
Equation 2 Standard deviation
As the number of observations is increased for a mean, its uncertainty is decreased. The meaning of
standard deviation for an X-bar refers how well determined that X-bar is. This is defined by Equation 3:
n
x
X
σ
=σ
Equation 3 Standard deviation of a mean