Physics and Radiobiology of Nuclear Medicine

Mean and Standard Deviation

When a series of measurements is made on a radioactive sample, the most
likely value of these measurements is the average, or meanvalue, which is
obtained by adding the values of all measurements divided by the number
of measurements. The mean value is denoted by.
The standard deviation of a series of measurements indicates the devia-
tion from the mean value and is a measure of the precision of the mea-
surements. Radioactive decay follows the Poisson distribution law, from
which one can show that if a radioactive sample gives an average count of
, then its standard deviation sis given by
(4.1)

The mean of measurements is then expressed as

Gaussian Distribution

If a series of measurements are made repeatedly on a radioactive sample
giving a mean count , then the distribution of counts would normally
follow a Poisson distribution. If the number of measurements is large, the
distribution can be approximated by a Gaussian distribution, illustrated
in Figure 4.1. It can be seen that 68% of all measurements fall within one

n

n±s

s= n

n

n

Mean and Standard Deviation 35

Fig. 4.1. A Gaussian distribution of radioactive measurements. Note the 68%
confidence level at ± 1 s, 95% comfidence level at ± 2 s, and 99% comfidence level
at ± 3 s.