In the last blog I mentioned riding on the shuttle seated next to a PhD candidate in statistics. One of the startling pieces of information for me is that the Common Core educational curriculum includes sections on statistics and probability at the high school level.
That is fantastic.
I then realized that I have three fundamental ideas that I attach to statistics and I wonder if they are taught in the Common Core curriculum.
The first is the law of large numbers. This must be learned at a gut level as do my two other fundamental statistical understandings.
If one fills up a series of small bags with beach pebbles and weighs each bag, the weight of all the bags together will be nearly identical to the average weight of each of the separate bags when totaled. This is something that is not obvious and must be understood at a gut level.
The second gut understanding deals with variance. Variance is a fundamental statistical concept. If a student is shown one set of 10 numbers but all of them are between one and nine (4,9,5,2,3,8,6,1,1,2) and also shown a series of 10 numbers with the various numbers between one and 100, (43,25,61,38,71,72,55,48,51,60) can the student look at the two sets of numbers and understand that the first set could have more variance than the other regardless of the range of numbers? Again a concept that needs to be understood at a gut level.
Lastly, can a student look at two sets of numbers and recognize one as human made and the other as random generated. ( I have found this to be another gut level and very important statistical understanding. (43 25 61 08 71 72 55 48 91 60).vs.. (10 41 48 53 37 85 14 99 69 35) The first set of numbers is human created. The second is random from a table of random numbers.