Interesting question! I've never thought about it before.
Well in an imaginary world where all the professional users of statistics found out about my opinion and agreed with me immediately,
the simplest change would probably be to make them hyphenated words:
- statistical-average
- statistical-normal
- statistical-norm
However, its unlikely that most people would continue to use a long hyphenated word. They might start off with those words, but they would probably start dropping the “statistic” part of the hyphenated words further on in their papers, lectures or conversations. So I would also suggest shorten versions of the hyphenated words that don’t currently exist in the English dictionary:
Professional users of statistics might agree to this change because there would be advantages including:
More precise meaning
I’ve been taught that one of the reasons that professional jargon is common is because it allows people to communicate and to be sure that everyone in the conversation is interpreting it the same way. They may not agree with each other, but at least they can agree on what the conversation was about.
Help make conversations and writings less emotionally charged.
Statistics is used in many studies including studies about people. It would probably help everyone stay on topic if less emotionally charged words were used. Average and normal do have different meanings in everyday language and if used in a conversation about people, those different meanings probably can’t help but bleed over to the conversation even if most of the people involved know that the statistical meanings are the ones that are suppose to be used at the time.
FWIW, although I accept and use the mathematical meaning of those words, it still grates on me. I don’t like it but I deal with it. When I talk about those topics I do try to use other words like ‘mean‘, ‘rare’ and ‘more common‘.
It’s usually not a great solution -- most people don’t remember that mean can be a synonym for average and not just a way to describe someone‘s behavior. People are also not used to using the words ‘rare’ and ‘more common’ when discussing statistics and the unusual use of those words can distract from the conversation.
But I believe that certain topics carry enough unwarranted baggage as it is, including the topics of hearing loss and deafness*, so I sometimes use those words anyway. But I would prefer to use statistical-average, statistical-normal, statistical-norm, staverage, and stormal.
And you know what? I could start using statistical average and statistical normal right away (unhyphenated). Next time I have a conversation involving statistics I think I will. Everyone would understand what I mean and the worst that could be said is that some people will think I sound wordy.
*Note: I have seen people who are not familiar with statistics, hearing loss and deafness look embarrassed when the statistical meanings of the words 'normal' and 'average' are used in conversation.