September 2025

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.

Five numbers, one argument: min, Q1, median, Q3, max. A boxplot is a headline about where most of the data lives and how it leans. The median’s position tells you skew. The whiskers whisper about range. Dots outside the fence ask for investigation, not exile. Compare groups side by side and you’ll see differences that

Variation tells you how bumpy the road is. Standard deviation (SD) captures bumps everywhere; the IQR focuses on the middle 50%. When life is skewed (lateness, income, completion time), IQR is a steadier compass: it ignores the cliffs and measures the lane. Say it plainly: “Half of students finished between 12–16 minutes (IQR = 4).”

Every dataset asks a simple question: will you let one number move the story? The mean listens to everyone… including the loudest guest. The median keeps its balance even when someone shouts. Neither is “better.” They’re different kinds of fairness. If you’re setting policy where a few extreme values would distort resources, lean median. If

1) Sort, Then Chart  A sorted table makes the chart inevitable. If your bars are jumbled, your point is too. Sort by the message you want to deliver and the design mostly designs itself. 2) Baseline on Purpose  Choose the baseline to tell the story… just be honest about it. Baseline choice is narration; clear disclosure keeps

A scatterplot is where relationships come to tell the truth. Start with four questions: direction (up, down, none), form (straight, curved), strength (tight, loose), and outliers (the rebels). Don’t rush to a trendline; earn it by describing the shape first. If the dots stack, add a touch of jitter or adjust transparency. Scale both axes