Troxler 4640-B, Operation And Instruction Manual

Page: 76 / 140

RADIATION STATISTICS
Radioactive emission is a random process. The number of emissions
in a given time period is not constant but varies statistically about an
average value. The variation about the true mean value is a Poisson
distribution. In this distribution, the standard deviation (
σ
) about the
mean (n) is defined as:
σ = √
n
When the mean is greater than 100, the Poisson distribution can be
closely approximated by the normal distribution (Figure A–2). The
normal distribution predicts the probability that any given count rate
will fall within a selected region about the mean.
NORMAL DISTRIBUTION
MEAN
3σ
68.3%
95.4%
99.7%
-3
σ
-2
σ
-1
σ
3
σ
2
σ
1
σ
Figure A–2. Variation of Radioactive Emission
Using the mean of a larger number of counts to approximate the true
mean, the distribution shows that 68.3% of the time the count rate
obtained will be within
±
1 standard deviation of the mean. Figure
A–2 shows the chance of counts falling within three standard
deviations of the mean. The user may perform a statistical stability
test (stat test) to compare the experimental standard deviation to the
theoretical standard deviation (see page 6–5).
Appendix A–4