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.
They are all the same.
Not necessarily.
If it is a symmetric distribution, the median must be 130.
how do i find the median of a continuous probability distribution
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
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).
(10, 15, 15, 15, 20) The answer above displays a sample in which the sample mean, sample median and sample mode assume the same value. If you were asking about populations, then the population mean, population median and population mode are the same whenever the probability density function for the population is symmetric. For example, the normal probability density function is symmetric, the t and uniform density functions are symmetric. Many are.
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.