"Is it possible to create a data set where $\bar{x}=30.0$, range $R=10$, and variance $s^2=40.0$?"
I feel sort of dumb asking this question, but I'm not quite sure I'm on the right track. I know that with two data points, the max variance is $50$ if $x_1=25$ and $x_2=35$, and then when adding a third point, variance seems to drop to a maximum of around $33$ if I stay within the range.
Is that correct, and is there a more mathematical way to show what I've said? The most we've been given so far is the equation for sample variance, mean, and a couple paragraphs on what a standard deviation is.