The mean would also not correspond to that definition, as the mean is just the way we would usually think of an average (add the data points together and divide by the number of data points).

The removal of the top and bottom 1% of the data isn't relevant to whether its a mean, median, or mode - its just a good way of getting a more representative measure of the population by excluding outliers. Often one might take what's called an "inter-quartile mean", the average excluding the top and bottom 25% of the data. In significantly large datasets (ie, the size of whole populations), it may be enough to simply exclude the top and bottom 1%!

Either way, your sentiment is in the right place, I just like maths and it's worthwhile making sure everyone is using the same words for the same things 😄