If the statistics in this course feels hard, it is often not the statistics. It is that the arithmetic underneath it is taking up all the room — and there is nothing left over for the actual idea. This is a place to fix that, quietly and on your own.
Every problem is generated fresh, so you will never run out and you cannot memorise your way through. Nothing here is graded, nothing is collected, and no one but you ever sees it. Get one wrong and you get the worked solution straight away.
The mean, and what you can do with it Start here — Averages, working backwards to a score you need, and combining two groups of different sizes.
These are the two extensions we did in class, plus the sense of how an average behaves that makes them obvious rather than fiddly.
Functions: domain and range — Which inputs a function will accept, and which outputs it can produce, across each family.
Almost everyone here has finished AP Pre-Calculus, and functions are where the gaps show. A model is a function, so reading what it will and will not accept is the difference between a prediction and a nonsense answer -- and the same reflex tells you a proportion cannot be 1.4 or a count cannot be negative.
Systems of linear equations — Two equations, two unknowns — by substitution, by elimination, and by graphing.
Two facts and two unknowns is the shape of more of this course than it looks. The combined-mean questions in the first strand are exactly this once you know the total and want the group sizes, and in Unit 5 the least-squares line itself is what comes out of solving two equations at once. It is also the algebra most likely to have gone quiet over the summer.
Fractions, decimals and percents — Moving between the three forms, and telling at a glance which of two numbers is bigger.
A probability turns up as 0.15, as 3/20 and as 15% on the same page. Every second spent converting is a second not spent thinking.
Estimating and sanity-checking — Ballpark answers without a calculator, and spotting an answer that cannot possibly be right.
The most valuable habit in this course: knowing roughly what the answer should be before you compute it, so a slipped decimal point announces itself.
Order of operations, rounding and roots — The machinery every formula in this course is built out of.
A z-score worked in the wrong order is not nearly right, it is wrong. Rounding halfway through does the same damage more quietly.
Ratios, rates and proportions — Parts of a whole, scaling a rate up and down, and part-over-total as a decimal.
Two-way tables, conditional probability and every “what fraction of the sample” question are proportional reasoning in a statistics costume.
