SAT Problem-Solving & Data Analysis Formula Sheet
Ratios, percentages, statistics, and probability formulas tested in the Problem-Solving & Data Analysis domain on the Digital SAT.
Below are the 12 formulas tested in this category, with the situation each one applies to. Drill until you can write the whole sheet from memory in under two minutes — that's the standard top scorers reach by test day.
Each formula links back to the topic page where it's worked into example problems. If a formula doesn't yet feel automatic, click into the topic page and grind that topic's six practice questions.
Formulas
| Concept | Formula | When to use it |
|---|---|---|
| Mean (average) | mean = sum / count | The "balance point" of the data. |
| Median | middle value of sorted data | For an even count, average the two middle values. |
| Range | range = max − min | Crude measure of spread. |
| Probability of an event | P(A) = favourable / total | Equally-likely outcomes. |
| Addition rule (mutually exclusive) | P(A or B) = P(A) + P(B) | When A and B cannot both happen. |
| General addition rule | P(A or B) = P(A) + P(B) − P(A and B) | Allows overlap. |
| Multiplication (independent) | P(A and B) = P(A) · P(B) | A doesn't affect B. |
| Conditional probability | P(A | B) = P(A and B) / P(B) | Probability of A given B happened. |
| Percent of | percent · whole | Part = percent × whole. |
| Percent change | (new − old) / old × 100% | Increase or decrease. |
| Unit rate | quantity / 1 unit | Compare different sizes fairly. |
| Margin of error idea | wider sample interval ⇒ less precise estimate | Bigger sample = smaller margin. |
How to memorise this sheet in a week
Day 1. Read every row out loud. Connect each formula to a worked example by clicking into the topic page on which it appears. Goal: understand why each formula is true, not just memorise it.
Day 2. Cover the right-hand columns and quiz yourself on each concept. Write the formula and the use case from memory. Mark the ones you missed.
Day 3. Re-quiz only the ones you missed yesterday. Keep cycling until your error count hits zero.
Day 4. Re-do the full quiz. You should know every row.
Day 5. Apply each formula in a problem context — pick a topic page from the list below and solve all six questions.
Day 6–7. Sit a real past paper. Note any formulas you blanked on under time pressure and add them back to your daily quiz.
Topics that use these formulas
- Ratios and Units6 Qs
- Percentage Problem-Solving6 Qs
- Mean, Median and Mode6 Qs
- Standard Deviation and Spread6 Qs
- Scatterplots and Trends6 Qs
- Two-Way Frequency Tables6 Qs
- Probability Basics6 Qs
- Conditional Probability6 Qs
- Sampling and Margin of Error6 Qs
- Data Inference and Conclusions6 Qs
- Line of Best Fit6 Qs
- Linear vs Exponential Models6 Qs
Common mistakes when applying these formulas
Three errors account for the majority of dropped points on formula-driven questions:
- Substituting before simplifying. Always simplify symbolically as far as you can before plugging numbers in. It cuts arithmetic errors in half.
- Mixing units. If a formula expects metres and you have centimetres, convert first, not at the end. The number you compute is meaningless until the units agree.
- Forgetting the ½ in area or volume formulas. Triangle, trapezoid, sector, cone, pyramid — all have a ½ or ⅓ that's easy to drop. Write the formula on the page before plugging in.