INTRODUCTION TO COUNTING STATISTICS

The Random Nature of the Decay Process

To illustrate the statistical variation associated with the measurement of a radioactive sample.

The Random Nature of the Decay Process

1. Select a long-lived laboratory reference source that will produce a low count rate (in the order of 100-200 cpm) on your counting station.
2. Take 40 (or more) successive 1/2 minute observations.
3. Repeat, using a source which yields more than 1000 cpm.

The Random Nature of the Decay Process

1. Plot a "scatter plot" of the data: counts recorded for each observation on the vertical axis, observation number (1 to 40) on the horizontal.
2. Calculate the mean value m of each limited (40 count) sampling.
3. Indicate the mean value on the data plot with a horizontal line at the appropriate value.
4. Evaluate the deviation of each count (n-m).
5. Does your data pass Chauvenet's criteria?
6. If not, correct the data set by eliminating the offending data point(s).
7. Evaluate the sample variance:

   

8. (Where j = number of observations.)
9. Evaluate the sample standard deviation.
10. Calculate the standard deviation based on the use of the sample mean:.

    

11. Indicate the ± 1, 2, and 3 standard deviation bands on the data plot with horizontal lines.
12. How well do the 40 sample sets conform to the GAUSSIAN model?
13. What percent of the mean (m) does the standard deviation represent for the low-count sample?
14. For the high-count sample?

Evaluation of Measurements

To illustrate the statistical variation associated with the measurements of a radioactive sample.

Evaluation of Measurements

1. Remove all samples from the immediate area of the detector.
2. Take a one-minute count, and a ten-minute count, for each of the three following situations:
   • Laboratory background, no source in detector.
   • "low-activity" source in detector.
   • "high-activity source in detector.
3. Repeat , if time allows, with a "high" background produced by an adjacent source.

Evaluation of Measurements

1. Evaluate each background count rate and its standard deviation, in cpm.
2. Evaluate each source count rate and its deviation , also in cpm.
3. For each combination of source count and background count, determine the net count rate attributable to the source, and its standard deviation.