The best measure of center for this data would be the Median, because there is an outlier. The median is less affected by an outlier than the mean would be. We find the mean by lining the numbers up from least to greatest and locating the middle number.
[tex]\sf 0, 1, 2, 4, 4, 5, 5, 24[/tex]
[tex]\sf 0, 1, 2,\boxed{\sf 4, 4}, 5, 5, 24[/tex]
So the median here is 4.