# SAT Problem-Solving and Data Analysis: Guide | topin

SAT guidesProblem-Solving and Data Analysis

Section

Math, about 15% of questions (5–7 scored)

Skills

Ratios, rates and units; percentages; one- and two-variable data; probability; sampling and margin of error; evaluating studies

Formats

Multiple choice and typed answers, often with a table or graph

Calculator

Allowed; useful for percentages and statistics

## How it works

These questions put maths in a context: a recipe scaled up, a price after a discount, a table of survey results, a scatterplot with a line of best fit. Hard versions ask how the mean, median or standard deviation change when a value is added or removed, what a margin of error does and does not mean, or what can be concluded from random sampling versus random assignment.

## Worked example

A shop raises the price of a lamp by 25%. During a later sale, the new price is reduced by 20%. The sale price is what percent of the original price?

1. A95%
2. B100%
3. C105%
4. D45%
Show the answer

B: 100%

Successive percentage changes multiply. A 25% rise multiplies the price by 1.25, and a 20% cut multiplies it by 0.80: 1.25 × 0.80 = 1.00, so the sale price is 100% of the original. Check with a number: £80 rises to £100, and 20% off £100 is £80\. 105% comes from adding +25% and −20%; 95% and 45% come from other ways of combining the two percentages directly.

## A method for Problem-Solving and Data Analysis

1. 1  
### Convert percentages to multipliers  
An increase of p% multiplies by 1 + p/100; a decrease multiplies by 1 − p/100\. Chain changes by multiplying, never by adding.
2. 2  
### Carry units through  
Write units with every number and cancel them as you go, especially for rates and conversions such as kilometres per hour to metres per second.
3. 3  
### Read the table or graph before the question  
Check titles, axis labels, units and totals. For two-way tables, note whether the question asks for a fraction of a row, a column or the whole table.
4. 4  
### Know what statistics change  
An extreme value moves the mean more than the median. Spread measures such as range and standard deviation grow when values move away from the centre.
5. 5  
### Match the conclusion to the study design  
Random sampling lets you generalise to the population sampled; random assignment lets you conclude cause and effect. Neither one gives you the other.

## Traps to avoid

* Adding successive percentage changes instead of multiplying them.
* Finding the percentage of the wrong total, such as a row total instead of the grand total in a two-way table.
* Concluding cause and effect from an observational study.
* Reading a margin of error as covering every individual rather than the population estimate.

## Problem-Solving and Data Analysis FAQs

What statistics are on the SAT?

Mean, median, mode, range and the idea of standard deviation (you are not asked to calculate it), plus lines of best fit, sampling, margin of error and conclusions from studies.

How do I do percent change on the SAT?

Percent change is (new − old) ÷ old × 100\. For several changes in a row, multiply the multipliers, such as 1.25 × 0.80.

Is probability on the digital SAT?

Yes, usually from a two-way table: the chance of one category, or of one category given another (conditional probability).

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