They are all the same.
Mean
yes
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.
Mean
yes
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.
In a symmetric distribution, the mean and median will always be equal. This is because symmetry implies that the distribution is balanced around a central point, which is where both the mean (the average) and the median (the middle value) will fall. Therefore, in perfectly symmetric distributions like the normal distribution, the mean, median, and mode coincide at the center. In practice, they may be approximately equal in symmetric distributions that are not perfectly symmetrical due to rounding or sampling variability.
All equal.