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

Page: 131 / 170

FISCHERSCOPE
®
X-RAY 131
Description of the Characteristic Statistical Parameters Addendum
17 Addendum
17.1 Description of the Characteristic Statistical Parameters
17.1.1 Block Result
Parameter Description Equation
Mean value
Mean value of the single readings,
called arithmetic mean value . The
arithmetic mean value is the
summation of all single readings of
a measurement series (block/group),
divided by the number of
measurements
n
.
: Single readings
: Number of measurements per
block
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 the measurements
per block
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 block
: Single readings
n
: Number of measurements per
block
x
x
x
i
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