Determining how to define a rare coin given a large data set of the years pennies were made

Question

I have a data set where the year a penny was made was recorded. The data contains over $3$,$000$ observations so I will just give example data. The data is laid out as follows:

Year

2016 
1990 
1997 
2004 
2003 
1982 
2005

My goal is to determine how to define a rare coin.

I have tried the following using SAS but I would be open to analyzing the data using alternative software such as R.

proc univariate data=New cibasic;
   var Year;
   histogram Year;
run;

But of course the confidence interval of $(1997,1998)$ is for the population mean. How could I determine the confidence interval for an individual coin? The following graph indicates that a rare coin would have the year being around $1960$.

SAS also provides this output:

Perhaps this would imply a rare coin would be from $1972$ or earlier? Although, maybe it would be better to use the $1$% quantile to define what a rare coin is?

Answer 1

The histogram shows the distribution is far from normal, so you should ignore anything based on that assumption. You have to define rare. One approach would be a rare coin is one that comes from a year that less than $1\%$ of the coins were made in, so a year where less than about $30$ were made. That would be any coin prior to $1970$ or so. One approach would be the earliest $1\%$ of the coins, which would be prior to $1965$. You can adjust the percentage to taste, which will change the year cutoff a bit.