1. find the balance point for the points 0.3, 0.4, and 0.8. 2. which measure of center is indicated by the center of balance, the median, the mean, or the mode? 3. define what is meant by “measure of center.”

Remark
There are only 3 points. The 0.8 is a little bit skewed, but I would still use the mean.

Question 1
Mean = (x1 + x2 + x3)/3
Mean = (0.3 + 0.4 + 0.8) / 3
Mean = (1.5)/3 = 0.5

The balance point is 0.5

Question 2
It depends on what the data looks like. 
See the graph below

With 3 points, it's pretty hard to tell. I calculated the middle one as the mean and it is what I take to be the central tendency, but do not be surprised if it is not. You could pick he left graph but how would you decide where the mode or median were?

Question 3
The measure of the center is the central tendency. It is what you use to figure out the dominant point of how the central tendency is found. There are not enough points to pick either the mode or the median.