Question

Can two dot plots have the same median and range but not have completely different shapes?

Answer 1

Yes because the median and range are not a function of the totality of the sample set, the median is just value that is halfway of the set and the range is the difference of the highest and lowest value. As long as the lowest and highest value and the halfway value are the same in each set, the median and range will be equal no matter what the other values of the set are.