The foundations of statistics are very much based upon Galton observing:
"the middlemost estimate expresses the vox populi, every other estimate being condemned as too low or too high by a majority of the voters"
at a livestock weight guessing contest and conceiving of a measure to quantify normal variation: the standard deviation without the use of calculus.
To be sure this evolved to expressions that included an integral sign or two .. but the foundations were founded with no more than a Sigma and some division.
There's a stronger case for those than care to make it that statistics is more dependant on linear algebra, if one takes the view that statistics is about finding fewer lower dimensional fair representations of many higher dimensional values.
Calculus really should be thought of as dependent on linear algebra (the derivative of a function is the best linear function that approximates it; it just happens that in 1D the only linear functions are multiplication by a single number). Linear algebra seems like it would be far more useful than algebra 2 (things like conic sections?), trigonometry, and "pre-calc".
It's possible that you could do something like algebra (middle school)->geometry (maybe introduce the notion of a group here and focus more on symmetry and not so much on figuring out the missing angle/length in a complicated diagram)->linear algebra->probability/statistics. Concurrent with linear algebra, have kids learn calculus in physics class. After physics 1, they can do chemistry and/or e&m. Do vector calculus in e&m. Basically trim all the useless stuff out of high school and add the first couple semesters of college instead. Offer analysis as an elective after linear algebra/physics 1, and put a proper account of the n-D derivative and things like the Newton–Raphson method there.
Obviously that's a STEM bound curriculum, but at least in my school growing up, you only needed algebra 1 and geometry to graduate, which the honors kids did in middle school. So I assume any curriculum more advanced than that is for STEM bound kids.
"the middlemost estimate expresses the vox populi, every other estimate being condemned as too low or too high by a majority of the voters"
at a livestock weight guessing contest and conceiving of a measure to quantify normal variation: the standard deviation without the use of calculus.
To be sure this evolved to expressions that included an integral sign or two .. but the foundations were founded with no more than a Sigma and some division.
There's a stronger case for those than care to make it that statistics is more dependant on linear algebra, if one takes the view that statistics is about finding fewer lower dimensional fair representations of many higher dimensional values.