Consider the following data set: 3, 4, 6, 7, 9, 9, 11. identify a number you could add to the set to keep the mean smaller than the median.

The mean is simply the average of the data set. 

Mean = (3+4+6+7+9+9+11)/7 = 7

The median, on the other hand, is the middle data when you arrange them from least to greatest. The middle data here is 7. 

Hence, initially, the mean and median are equal. In order to make the mean less than median, add another data point which makes it the lowest. For example, we can add 1 as the new data point. The mean would be:

Mean = (1+3+4+6+7+9+9+11)/8 = 6.25

The median is (6+7)/2 = 6.5

Therefore, you can add any number less than 3. For example, that could be 1.

You take to two numbers in the middle and add then (2+4) and that equals 6 so that is your mean. then you take you 6 and then you divide it by 2 (6/2) and that equals, 3 and that is the median.