thought prompt

Numbers are shy until you sketch them. With the normal curve, the picture is the plan: mark μ and σ, shade the region, then choose the move… area or cutoff. Most errors aren’t math mistakes; they’re region mistakes. We solve for a left tail when we meant the middle. We read the wrong column. Drawing […]

1) Draw Before You Measure  If you haven’t drawn the scatterplot, you haven’t earned r. Shape first, number second. 2) Check the Residuals  If the residuals curve, your relationship did too. Fit ideas, not just lines. 3) Try Spearman When Life Bends  Monotonic but curved? Spearman respects order without demanding straightness. 4) Simulate Your Intuition  When a probability feels

“Independent” does not mean “unrelated in spirit.” It means: knowing one outcome tells you nothing about the other. Dice rolls? Independent. Midterms and sleep? Probably not. Don’t confuse mutually exclusive (can’t both happen) with independent (don’t inform each other). If events are mutually exclusive and both have positive probability, they are not independent. Start with

A probability isn’t a prediction; it’s a contract about the long run. “Thirty percent rain” 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

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. That’s why Anscombe’s 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

An outlier with long arms (extreme x) can drag your regression line across the room. That’s leverage… and it talks louder than the rest. Before you trust r or a slope, label the loud points and ask three questions: (1) Is it real? (2) Does it represent a scenario we care about? (3) What happens

Pearson’s r only loves straight lines. Real life loves curves. When the relationship bends, r shrugs… even if the pattern is obvious. The fix isn’t a fancier formula; it’s a better question. Describe the shape first (up, down, bends where?), then choose a summary that respects it: Spearman for monotonic curves; a transformation if the

1) Report Two Centers When Skewed  If the tail is long, report both mean and median. The gap is the story. 2) Write the Five Numbers  Before plotting, write min, Q1, median, Q3, max on a sticky note. If the note is clear, the chart will be. 3) Outliers: Trim, Transform, or Tell  Three honest moves: investigate and

Correlation tells you where the dots like to travel, not why they travel. Direction, form, strength, and the rebel points… that’s your checklist. Don’t rush to r; earn it by describing the shape. If one point has long arms (extreme x), it can drag the line… note it. If the shape bends, say “curved,” not

A raw score is a place on a ruler; a z-score is a place in a crowd. Standardizing turns “82” into “+1.1,” which turns into, “about the 86th percentile… ahead of most peers.” That’s communication. Use z-scores to compare across different scales (points vs minutes vs questions right) and to spot the unusual without guessing.