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Statistical Consulting Centre : Department of Mathematics and Statistics
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The effect of eliminating 1 and 2 cent coins

In 1994 1 and 2 cent coins were taken out of circulation in Australia. Today all hard cash transactions are rounded to the nearest 5 cents. Should shopkeepers be worried about losing a lot of money due to rounding?

What are the effects on shopkeepers?

As an example, consider a shopkeeper after 1000 transactions (about 50 per day for a month of 20 trading days). Rounding to the nearest 5 cents, any given shopkeeper will expect to break even. However, some will make a bit and some will lose a bit. What is a range within which 95% of shopkeepers will be after 1000 transactions? Bear in mind, the most unlucky shopkeeper would lose 2 cents on each transaction, for a total of $20.

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This graph shows the fortunes over time of 5 shopkeepers (each in a different colour) as simulated by a computer. The curved black line shows the 95% range for all shopkeepers.

Very surprisingly, 95% of shopkeepers will gain or lose no more than 88 cents in 1000 transactions. Only 1.15% of shopkeepers (one in 87) will lose more than $1 in 1000 transactions, and 0.06% (four in 10,000) will lose more than $1.50. These results are found using the "Central Limit Theorem", a key result in probability.

What are the effects on large supermarkets?

Should large supermarkets that do, say, one transaction each minute, 12 hours a day, 7 days a week, 365 days a year, for a total of 262,800 transactions in a year worry about losing a lot of money?

Even though losing two cents on each transaction would give a loss of $5256, 95% of such large stores will be within $14.21 of breaking even at the end of the year! The 95% range grows slowly, as the square root of the number of transactions. So, for example, after 100,000 transactions the 95% range doesn't increase to $88 from 88 cents (100 times 88 cents) but rather to $8.80.

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