Ignoring values in a sum list

Hi, 

I have to run sums on discrete cells in an analytical report.  If the data is reported at below detectable level, they report it as <1 or <10

Thus how do I create a sum function where the data could be 

10, 15, <1, ,<10, 20 to produce a result of 45?

Please help, I have been wrestling with this for years.