A z-score is a distance in standard deviations… a unit of surprise. āz = +2ā means ātwo Ļ above typical,ā not āsmartā or āgood.ā Use z to compare across scales (minutes, points, dollars) and to speak percentile without the drama. The trick isnāt memorizing every table entry; itās knowing where the tails start to matter […]
Z-Scores Are Units of Surprise Read More Ā»
Hereās the repeatable sequence: draw ā set Ī¼ & Ļ ā pick region ā choose area or value ā compute ā translate. If you need a probability, compute an area. If you need a cutoff, get a value. The workflow isnāt fancy; itās protective. It keeps you from solving the same problem six different ways
One Workflow to Rule Your Bell Curve Read More Ā»
Numbers are shy until you sketch them. With the normal curve, the picture is the plan: mark Ī¼ and Ļ, shade the region, then choose the move… area or cutoff. Most errors arenāt math mistakes; theyāre region mistakes. We solve for a left tail when we meant the middle. We read the wrong column. Drawing
Draw the Curve Before You Decide Read More Ā»
1) Draw Before You MeasureĀ Ā If you havenāt drawn the scatterplot, you havenāt earned r. Shape first, number second. 2) Check the ResidualsĀ Ā If the residuals curve, your relationship did too. Fit ideas, not just lines. 3) Try Spearman When Life BendsĀ Ā Monotonic but curved? Spearman respects order without demanding straightness. 4) Simulate Your IntuitionĀ Ā When a probability feels
Eight Tiny Experiments for Patterns First, Probabilities Second Read More Ā»
āIndependentā does not mean āunrelated in spirit.ā It means: knowing one outcome tells you nothing about the other. Dice rolls? Independent. Midterms and sleep? Probably not. Donāt confuse mutually exclusive (canāt both happen) with independent (donāt inform each other). If events are mutually exclusive and both have positive probability, they are not independent. Start with
Independence Isnāt Friendship Read More Ā»
A probability isnāt a prediction; itās a contract about the long run. āThirty percent rainā means: if you could replay today a thousand times, it would rain in about 300 of them. On any single day, reality is lumpy. Act like a portfolio manager: define the sample space, list outcomes, assign fair odds, and make
Probability Is a Contract, Not a Crystal Ball Read More Ā»
Two very different clouds can share the same correlation. One may be tight with a rebel; the other, loose but clean. Numbers rhyme; pictures speak. Thatās why Anscombeās lesson endures: always sketch the data. Write one sentence for each plot: direction, form, strength, outliers… and only then compute r. If your sentence and your statistic
Same r, Different Story Read More Ā»
