Mass & Benford’s Law

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Mass & Benford’s Law

On March 17, 2009, Posted by , In operations research,statistics, With No Comments

Here in Spain it’s usual that a part of the mass is what we call the ‘cepillo’ (donations). How much is the total ‘collection’?. If we assume no notes are handed over and we can’t sumise the coin value for its ‘clinck’, one of the possibilities we have in order to estimate the total collection is:


1) Count the number of coins based on the number of ‘clincks’.

             Sup. 1 ‘clinck’ = 1 coin

2) Consider Benford’s Law to estimate the distribution of the coins.



Starts with


of occurence

1 30.1%
2 17.6%
3 12.5%
4 9.7%
5 7.9%
6 6.7%
7 5.8%
8 5.1%
9 4.6%


         Here in Europe we have coins of 1c, 2c, 5c, 10c, 20c, 50c, 1 EUR, 2 EUR. So, the previous table could be re-written (n.b.: guesstimation):




of occurence

1c, 10c, 1 EUR

(Simple Average = 37c)

54.1 %

2c, 20c, 2 EUR

(Simple Average = 74c)

31.7 %

5c, 50c

(Simple Average = 27.5c)

14.2 %


Other possibility is to wait until the end of the fiscal year and expect your Parish will make available the collection figures and try to estimate a weighted average for a normal Sunday. And we’ll be having better information, since the method is quite flawed, starting for the distribution of coins in the pocket may follow a uniform distribution, plus the simple averages used in the second table don’t make any sense. However, this is a starting point.


Disclaimer: I attended a Catholic School, I even tutorised church lessons for two years while in High School; I’m very respectful to any religion, including Catholicism, whenever they are respectful to the rest. This was just an exercise of applying OR to another normal aspect of life.