Provide an appropriate response.Explain how two data sets could have equal means and modes but still differ greatly. Give an example with two data sets to illustrate.

Question

What will be an ideal response?

Answer 1

Answers will vary. The two data sets could have equal means and modes while having very different amounts of spread (variation) around the mean. For example, the following two data sets have equal means and modes but differ greatly as they have very different amounts of spread. 
Data set I: 48, 49, 50, 50, 51, 52 (mean and mode both equal 50)
Data set II: 10, 30, 50, 50, 70, 90 (mean and mode both equal 50)