Can two box plots have the same range and inter quartile range and yet represent completely different data?

Yes, two box plots can have the same range and interquartile range (IQR) while representing completely different data sets. The range indicates the difference between the maximum and minimum values, while the IQR measures the spread of the middle 50% of the data. However, the overall distribution, outliers, and specific quartile values can differ significantly, leading to variations in the shapes and characteristics of the data sets they represent.