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Math · 16 · Problem-Solving and Data Analysis

Statistics

Notes

Key points

  • Line of best fit predicts: read the line, not the nearest data point.
  • Slope of the fit line = predicted change in y per 1 unit of x.
  • Positive, negative or no association; strong = points hug the line.
  • Residual = actual − predicted. Above the line → positive residual.
  • Linear: adds the same amount each step. Exponential: multiplies by the same factor.
  • Table: constant differences → linear; constant ratios → exponential.
  • Desmos: data in a table, then y1∼mx1+by_1\sim mx_1+b.

Formulas

Linear modely=mx+by=mx+bSame difference per unit
Exponential modely=abxy=ab^xSame ratio per unit
Residualactual−predicted\text{actual}-\text{predicted}
Percent growth per stepb=1+rb=1+rb = 1.05 means 5% per step

Common traps

  • Giving the actual value when the question asks for the predicted one.
  • Concluding causation from a scatterplot — it only shows association.
  • Calling “increases 5% each year” linear. Percent change is exponential.

SAT tip

“Predicted” or “estimated” on a scatterplot means use the line of best fit at that x, not the plotted point.

Test yourself

10 official SAT questions on Statistics, easiest first.

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