Question

Can two box plots have the same range and iqr and yet represent completely different data

Answer 1

yes

Explanation:

One data set could range from 100 to 150, and another data set could range from 10 to 60. Both have a range of 50. The first data set could have quartiles at 120 and 130 and the second data set at 20 and 30, with both IQRs equal to 10.

Answer 2

as far as I can tell yes just as long as your range and mean don't change