yes
Mean
That would provide some evidence that the distribution is symmetric about the mean (or median).
Only if the dataset (distribution) you are dealing with in symmetric.
Not necessarily.
In a symmetric distribution, the mean and the median are the same. Otherwise there is no relation. In symmetric distributions with only one mode, the mode will coincide with the mean and median, but otherwise there is no relation.
If it is a symmetric distribution, the median must be 130.
No. The mean and median are not necessarily the same. They will be the same if the distribution is symmetric but the converse is not necessarily true. That is to say, a distribution does not have to be symmetric for the mean and median to be the same. For example, the mean and median of {1, 1, 5, 6, 12} are both 5 but the distribution is NOT symmetric.
Yes, they can.Yes, they can. In a symmetric distribution they will be the same.
yes
Mean
That would provide some evidence that the distribution is symmetric about the mean (or median).
That would provide some evidence that the distribution is symmetric about the mean (or median).
Median.
Yes. And in any symmetric distribution, they will.
If the distribution is not symmetric, the mean will be different from the median. A negatively skewed distribution will have a mean hat is smaller than the median, provided it is unimodal.
All equal.