48
2 Analytical Properties
fr
sIal =
~ })X_X)l
n-1
data
The standard deviation is a measure of the proportion of data that can exist within a given
interval around the mean.
Interval
p ± a
p ± 1.96a
p ± 2.57a
p ± 30
p ± 3.290
% DATA
68
9S
99
99.7
99.9
• Variance: the standard deviation squared (52, 0 2 )
• Relative standard deviation
• Coefficient of variation (a percentage)
CV = rsd · 100
• Sta ndard deviation of the means
- Means (Xt'x2, ... ) resulting from grouping data for samples of the same population.
- The mean of these means is Xm; their standard deviation (sdm) does not coincide with
that of the population (0,5).
0 (5)
sdm= - .In
The greater n, the lower the dispersion among the means
- When n -7 00, sdm -7 0 (all measurements tend to provide the same result)
- sdm is a measure of the uncertainty incurred in estimating p from x
• Limits of confidence for the mean
- The interval within wh ich a given measurement can be assumed to fall with a preset
likelihood or the va lue held as true, p, to lie when an analytical process is repeated.