172
11 Statistics of Counting
before crossing the river measured the depth of water at various places (i.e., across
the river) and calculated the average depth to be 90 cm. The youngest member of the
family being 105 cm in height, the leader decided to cross the river with all members.
To the utmost surprise to the leader, everyone except the leader was drowned, when
they reached the middle of the river because the depth of the river at someplace
was greater than the average depth of 90 cm. Thus, the average does not give any
idea about the maxima and the minima deviations from the mean. Therefore, while
representing a data, it is advisable to represent the variation in mean also.
The decay of radioactive isotope being a random process, it is extremely unlikely
to obtain two consecutive count rates same value even for a long-lived isotope. Under
such conditions, how do we represent an activity of a radioactive isotope accurately?
In this chapter, we shall deal this question in somewhat detail.
11.2 Statistical Error in Counting
Before we can understand the significance of statistical error in counting, it may
be appropriate to examine a set of counts recorded by counting a very long-lived
isotope (i.e., during the course of counting, there should be no appreciable change
in the activity). A radioactive Carbon-14 source was counted by a Geiger-Müller
counter. Counting was done for 1 min duration for several times (Table 11.1). It is
noticed that though during the period of counting of Carbon-14 (i.e., in about 45 min),
there should be no change in the activity, but almost all counts have different values
ranging from 9650 to 10,059 cpm. Question is which of these counts should be
taken as a correct value? The average of these counts comes to 9742.5 cpm and it is
accepted as the correct value.
It is customary to calculate the square root of the average value which is 98.70
cpm. We take this value as a range and then between the maximum count rate (i.e.,
Table 11.1 Count per minute recorded with C-14 sample with a Geiger-Müller counter
Counts per minute
9858
9648
9700
9652
9744
9840
9700
9800
9659
9839
9765
9795
9645
9709
9708
9713
9800
9709
9721
9748
9679
9759
9710
9718
9809
9763
9841
9778
9840
9903
9615
9755
9740
9762
9775
9756
9753
9752
9552
9557
11 Statistics of Counting
before crossing the river measured the depth of water at various places (i.e., across
the river) and calculated the average depth to be 90 cm. The youngest member of the
family being 105 cm in height, the leader decided to cross the river with all members.
To the utmost surprise to the leader, everyone except the leader was drowned, when
they reached the middle of the river because the depth of the river at someplace
was greater than the average depth of 90 cm. Thus, the average does not give any
idea about the maxima and the minima deviations from the mean. Therefore, while
representing a data, it is advisable to represent the variation in mean also.
The decay of radioactive isotope being a random process, it is extremely unlikely
to obtain two consecutive count rates same value even for a long-lived isotope. Under
such conditions, how do we represent an activity of a radioactive isotope accurately?
In this chapter, we shall deal this question in somewhat detail.
11.2 Statistical Error in Counting
Before we can understand the significance of statistical error in counting, it may
be appropriate to examine a set of counts recorded by counting a very long-lived
isotope (i.e., during the course of counting, there should be no appreciable change
in the activity). A radioactive Carbon-14 source was counted by a Geiger-Müller
counter. Counting was done for 1 min duration for several times (Table 11.1). It is
noticed that though during the period of counting of Carbon-14 (i.e., in about 45 min),
there should be no change in the activity, but almost all counts have different values
ranging from 9650 to 10,059 cpm. Question is which of these counts should be
taken as a correct value? The average of these counts comes to 9742.5 cpm and it is
accepted as the correct value.
It is customary to calculate the square root of the average value which is 98.70
cpm. We take this value as a range and then between the maximum count rate (i.e.,
Table 11.1 Count per minute recorded with C-14 sample with a Geiger-Müller counter
Counts per minute
9858
9648
9700
9652
9744
9840
9700
9800
9659
9839
9765
9795
9645
9709
9708
9713
9800
9709
9721
9748
9679
9759
9710
9718
9809
9763
9841
9778
9840
9903
9615
9755
9740
9762
9775
9756
9753
9752
9552
9557