Really?
Why not 5% of Americans having the same average level of understanding and only 47.5% having a lower than average understanding?
What assumptions are you making, and why should they be true?
Why not 5% of Americans having the same average level of understanding and only 47.5% having a lower than average understanding?
What assumptions are you making, and why should they be true?
Average and mean are the same: normal distribution. Average higher than mean: skewed by big outliers.
Professional statistician affects the distribution of statistics knowledge like billionaires affect wealth distribution.
Again, why does the GP assume that a full half are distinctly lower than "average understanding" ? Why the assumption that multiple numbers cannot share an average understanding?
That said,
If the mean and median were the same your statement would still not be always true. For more than one reason.
I’m interested, in what cases would it not be true if we assume “average” here to be “median”? I can only think of one: if we consider “understanding” to be discrete rather than continuous.