2.3 Errors in Analytical Chemistry
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47
• The "sample" and "population" concepts as referred both to a set of aliquots (samples) of
an object and to the results obtained by subjecting each aliquot to an individual analytica l
process.
Aliquots (n)
Population
00 (n > 30)
Sample
n < 30
• Statistical processing of data (results)
- n measurements
Arithmetic mean
J.l'
- absolute frequency with which they occur
XI.X2.··· Xn
fl.f2 . ... fn
Standard deviation
a
5
- normal (Gaussian) distribution
bell-shaped plot of relative frequency
(fnln) as a function of the data.
(0) Characteristic of dispersion among data.
(b) Characterized by some mathematical terms
x
• Parameters that characterize a normal distribution of data
- Arithmetic mean (X and ]1').
data
- Standard deviation: the distance (to the right or left) from the mean to the fi rst
inflection point in the curve. The most elementary measure of dispersion (expressed
in the same units as the data).
, -,
,
,
/
,
I
\
I
\
I
\
\ (omputers ,
I
'-'
47
• The "sample" and "population" concepts as referred both to a set of aliquots (samples) of
an object and to the results obtained by subjecting each aliquot to an individual analytica l
process.
Aliquots (n)
Population
00 (n > 30)
Sample
n < 30
• Statistical processing of data (results)
- n measurements
Arithmetic mean
J.l'
- absolute frequency with which they occur
XI.X2.··· Xn
fl.f2 . ... fn
Standard deviation
a
5
- normal (Gaussian) distribution
bell-shaped plot of relative frequency
(fnln) as a function of the data.
(0) Characteristic of dispersion among data.
(b) Characterized by some mathematical terms
x
• Parameters that characterize a normal distribution of data
- Arithmetic mean (X and ]1').
data
- Standard deviation: the distance (to the right or left) from the mean to the fi rst
inflection point in the curve. The most elementary measure of dispersion (expressed
in the same units as the data).