Coin Comparisons

Australian and US coins have some similarities but many differences. Images and data are readily available on the “net” and make for rich areas of investigation. The following data was obtained from the Royal Australian Mint website, and Coins of the United States dollar on wikipedia.

The Australian coins currently in circulation, (as pictured above) are 5, 10, 20 & 50 cents (loosely referred to as silver coins); and 1 & 2 dollar (loosely referred to as gold coins). All are circular with the exception of the 50 cents which is a dodecagon. The “copper” 1 & 2 cent coins were withdrawn from circulation in Feb 1992.

The American coins in circulation are now all circular, and do not contain any gold or silver. I do however own a silver eagle, of which I am quite proud.

I wondered if there is any correlation between face value and either weight or size of the above coins? Here is a data table:

Creating scatter plots in Excel showed that there is little or no correlation present. In particular, comparing value to diameter:

1. Aussie Coins coefficient of determination (R squared) = 0.067, this increases to 0.80 if the 1 & 2 dollar coins are omitted.

2. US Coins coefficient of determination = 0.505 which increases to 0.984 if the 10 cent and 1 dollar are omitted.

Some further questions for investigation:

1.  Which country has a high correlation between the variables above?

2.  Are other variables more highly correlated eg. value of metal content

3.  What other shaped coins are used in other countries? See World Coins website.

4.  What change is possible for 1USD? 1AUD? 1 British Pound? (stayed tuned for next post!)

About webmaths

I have been teaching Mathematics in Victorian secondary schools for 30 years. I use the www to make my maths lessons better. I hope this blog will give other teachers some ideas to try in their own classes.
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