Question

A set of seven positive integers has a median of 3 and mode of 4. If two 2s are added to the set, the median and the mode of the new set are both 2. What is the mean of the new set?

Answer 1

I'm thinking that the original data set in ascending order might look like this:

____, ______, _______, 3, 4, 4, ________

Answer 2

For the new mode to be 2, after adding two twos, there must have been at least one two in the original data set.

____, ______, ___2____, 3, 4, 4, ________

Answer 3

Now, the two 2s are added:

_____, ______, __2__, __2____, ___2____, 3, 4, 4, ________

Here, there are now 9 elements in the set. The mode is 2 and the median is 2.