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.
Both 45/48 and 60/64 give you the same answer when you simplify them.
Well, experimental probability was used from what you have (info). It helps make predictions because you can use it for math etc.
I hope that’s right. Sorry if I got it wrong. Have a good day!