Problem-Solving & Data System

These questions are missed by misreading, not by maths — the fix is reading the graphic and the ask before touching numbers. Problem-Solving & Data Analysis is ~15% of Math and the domain where strong students bleed careless points: wrong denominator on a conditional probability, percent-of vs percent-change, median vs mean. Slow the read; the arithmetic is easy.

Sources: College Board math types; UWorld, Piqosity. Examples MERIDIAN-original. Point convention: each = 1 of ~44 Math; Module-1 misses are ceiling-risk.

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#WHAT IT TESTS

Ratios, rates, proportions, units; percentages; one-variable data (mean/median/range/spread); two-variable data (scatterplots, line/curve of best fit); probability and conditional probability (two-way tables); inference from samples + margin of error; evaluating study design (observational vs experiment).

#THE METHOD

1. READ THE GRAPHIC FIRST: title, axis labels, UNITS, legend.
2. READ THE ASK precisely: which group? per what unit? change or level? mean or median?
3. SET UP: proportion for rates; right denominator for conditional probability; estimate ± MOE for intervals.
4. COMPUTE (Desmos for mean/median/percent) and re-check the ask.

Why (mechanism): the traps are reading errors dressed as maths — a true data point that doesn't answer the ask, the whole-table denominator when the question conditions on a row. Reading graphic + ask first defuses them. [Most PSDA losses are −1 careless, not content — exactly the 1500→1600 leak.]

#TRAP TAXONOMY

• Wrong denominator (conditional probability): using the table total instead of the conditioning subgroup.
• Percent-of vs percent-change: "20% more than" ≠ "20% of."
• Mean vs median on skewed data: an outlier pulls the mean, not the median.
• Over-inference: generalising beyond the sampled population, or reading causation into a correlation/observational study.
• Unit mismatch: minutes vs hours, thousands vs ones.

#SAME ITEM, TWO LEVELS (MERIDIAN-original)

Two-way table: Of 200 people, 120 are adults (90 subscribe, 30 don't); 80 are minors (20 subscribe, 60 don't). "Given that a person is an adult, what is the probability they subscribe?"

• ~700 (trap): 90/200 = 0.45. Trap: wrong denominator — used the whole sample, not the adults. [−1; common careless loss]
• 800 (precise): condition on adults → denominator = 120 → 90/120 = 0.75. Move: identified the conditioning subgroup as the denominator. (Annotate "given adult" → denominator = adults.)

#DIAGNOSE YOUR ANSWER

• Conditional probability wrong? Wrong denominator. Fix: "given X" → denominator = the X group only.
• Percent wrong? Mixed up "of" and "change." Fix: change = (new−old)/old; "of" = percent×whole.
• Center wrong? Used mean on skewed data. Fix: outliers → median is the resistant measure.
• Inference too strong? You over-generalised or assumed causation. Fix: observational ⇒ association only; sample ⇒ only that population.

#DRILLS (timed · self-marked · MERIDIAN-original)

Drill 1 — Read-first (target 6/6, ≤4 min): for 6 graph/table items, write axis labels + units + the exact ask before choosing. PASS: no axis/ask misreads. Drill 2 — Conditional probability (target 5/5, ≤4 min): 5 two-way-table questions; write the denominator group first. PASS: correct denominator each time. Repetition: fail → repeat next day.

#TRANSFER

Abstract rule: read graphic + ask → set up (proportion / right denominator / interval) → compute → re-check the ask. Second context: a survey-results table and a lab-measurements scatterplot are the same read-first task. Constant: the method + trap list. Changes: the data context.

#REFERENCE CARD — PROBLEM-SOLVING & DATA

READ FIRST: title · axes · UNITS · legend · the exact ASK (which group? change vs level? mean vs median?)
Conditional prob = favourable / (conditioning subgroup)   ← right denominator
%change=(new−old)/old · %of=percent×whole · outliers → use median
Inference: observational ⇒ association only; sample ⇒ that population only
TRAPS: wrong denominator · %of-vs-change · mean-on-skew · over-inference · units
Each item = 1 of 44 Math Q; Module-1 miss = ceiling risk.

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MERIDIAN · FORGE · PROBLEM-SOLVING & DATA SYSTEM | v1.0