Count Rate and Standard Deviation
  1. Consider counting a sample over a period of time and note the following points
    1. The longer you count a sample the greater your counts
    2. The greater your counts the smaller the SD
    3. So how many counts are enough to be confident the a given value?
  2. The inherent error of measurement of any count rate is determined by the following formula where
    1. c = courting rate
    2. t = time over which the counts are acquired

    sd2sd countingrate.jpg - 5538 Bytes

  3. As an example let us say that you have acquired a total of 7345 counts in 5 minutes. What is the SD for this value at a 95% level of confidence?
  4. sd2sd countingrateex1.jpg - 6130 Bytes

  5. Based on the calculation above there is a 95% certainty that the true counting rate will fall between 7268 to 7422
    1. One should note that based on the above data if you increase your counting time you increase your level of accuracy
    2. HW - From the above data what are your SDs for 68% and 99%?

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