Statistics taught at earlier ages need not cover more than the arithmetic involved, not major concepts...however, reliability of the data can be introduced, especially querying students on whether they believe the database was large enough to draw a proper conclusion...these concepts are widened as the student grows in age and knowledge.  I could certainly see my 8th grade advanced math grandson being able to do standard deviation calculations...

Concepts have to be presented according to the age and ability of students.  Some are ready, some are not.