It's a bit difficult to answer the question as asked, though it's fairly easy to give specific cases where it is true.
One (although not the only) example would be when the data consist of a single value. If your dataset is (2, 2, 2, 2, 2) then the median, the mode, and the mean are all 2.
Another example that's a bit less trivial is (1, 2, 2, 2, 3) where again the median, the mode, and the mean are all 2.
Mean, median, and mode are all equal in a normal distribution.
Yes.
In a normal distribution the mean, median and mode are all the same value.
Yes, you can if you have 3 of the same number. For example, 33, 33, 33. Your mean, median and mode will be 33 for all the them.
Yes.
Mean, median, and mode are all equal in a normal distribution.
(10,10,30,30,30,50,50) (20,20,30,30,30,40,40) These two sets have the same mean, median and mode.
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.
Yes.
In a normal distribution the mean, median and mode are all the same value.
Yes, you can if you have 3 of the same number. For example, 33, 33, 33. Your mean, median and mode will be 33 for all the them.
who discovered mean median and mode
The normal distribution.
Yes.
They could all be the same number, e.g. 55555 (mean=median=mode=5) or they could be three numbers the same, with an equal space between the first two and the last two, e.g. 24446 (mean=median=mode=4). For the mode to be well-defined, some of the numbers have to be the same.
1,2,2,2,3
Yea