FISCHER FISCHERSCOPE X-RAY 4000 Series, Operator'S Manual

Page: 136 / 170

136 FISCHERSCOPE
®
X-RAY
Addendum Description of the Characteristic Statistical Parameters
17.1.3 Final Result – Variable Block Definition
Manual block creation (Block definition variable) is enabled for the product.
Parameter Description Equation
Mean value
Arithmetic mean value of the single
readings
: Single readings of the selected
blocks
: Number of measurements of the
selected blocks
Confidence
interval
q
Each measurement device produces
random measurement errors. With a
certain probability (confidence level),
the true value of the measured
parameter lies in an interval (double-
sided confidence interval) around the
measured mean value of a
measurement series (block/group).
The borders of this interval are at a
distance
q
from the true value .
q
is calculated according to the
equation below assuming a normal
distribution for a confidence level of
95 %:
t
: Quantile of the Student’s t-distri-
bution (Student’s factor), can be
obtained from tables in common
publications [1]
s
: Standard deviation
n
: Number of measurements of the
selected blocks
Standard
deviation
s
The standard deviation is a measure
of the dispersion of the single
readings of a measurement series
about the mean value.
: Mean value of the single read-
ings of the selected blocks
: Single readings of the selected
blocks
n
: Number of measurements
Coefficient of
variation
V
[%]
Standard deviation relating to the
mean value
s
: Standard deviation
: Mean value of the single read-
ings of the selected blocks
x
x
1
n
--- x
i
i 1 =
n

=
x
i
n

x

x q –

x q +
 
q t
f 1 0 025

– ;
s
n
------- =
s
1
n 1 –
------------ x x
i
–
 
2
i 1 =
n

=
x
x
i
V
s
x
-- 100 =
x