I don't think you can use that word analyzer as a standard benchmark!
For one, it's an american website so does not reflect UK usage, particularly.
Secondly, if you read how it works, it obtains its rankings via searching Project Gutenberg, so hardly an unbiased source, and only refers to written words in very specific published (and often highly edited) sources. It therefore doesn't reflect how often all people use a word in speech, just how often a small subsection of people write it
Thirdly, 'Project Guternberg' is hardly a realistic representation of how the everyday person understands or uses language! If it trawled through FB, twitter or online forums, maybe...!
For example, I searched words like 'netflix' 'wank' (and 'wanky'), barney (as in to have an argument') 'knobhead' and 'cuppa' - none of which came up with any ranking at all as they were deemed so unusual yet I would put money on being words better known to the British population at large than 'ameliorate.'
For what it's worth, 'bum' (with the same definition as in the UK) is ranked 12,330rd in usage and its understanding rated at collegiate level (e.g. 18 plus, university educated), compared to ameliorate at 10,303rd and with an expectation that it would be understood by the average person with a junior high education (e.g. aged 11-13)
Lies, damned lies, and statistics, etc.....