Leaving aside mathematical quibbles, in common speech we normally associate the middle with the average or thereabouts. However, when it comes to talking about income, the use of “middle” becomes so strange that it distorts public discussion.
Someone on, say, three times an average wage cannot sensibly claim the term “middle income”. The meaningful term is “high income” or “rich”. Those on greater multiples can be described as “very rich”, “filthy rich”, “obscenely rich” etc. etc. but NOT “middle income”.
Now, some rich people lay claim to the term “middle income” because they spend their money in a praiseworthy way (e.g. school fees, their home etc.) leaving little to spend on, say, entertainment and holidays. Such spending decisions might attract the terms, “prudent”, “sensible”, “family oriented”, but they have no bearing on categorization of income.