SAT Topics: Problem Solving & Data Analysis

The Problem Solving part refers to solving proportions, converting units, and other skills that we might call basic calculations. Roughly half of the problems in this domain fall into this category. The Data Analysis part refers to the other half. These questions all have something to do with statistics or probability.

Basic Calculations

Ratios, Rates, Proportional Relationships, and Units — Unit conversion problems don't typically give people trouble except when converting areas or compound units, i.e. measurements with denominators. If those sorts of problems give you trouble, you might want to brush up on the method of unit multipliers. You might also need to do word problems involving speeds or densities. Problems involving speeds, unit prices, and other rates are common. Here are the easy, medium, and hard practice problems from the SAT Practice Problem Databank.

Percentages — Sometimes the problem is as simple as "what is 10% of 470?", but that's not common. There are lots of stumbling blocks and sneaky tricks in this category, so be on your guard. Beware especially of the difference between a percentage of something and a percent greater than or less than something, especially with percents greater than 100. (Ridiculous triple-digit percents are fairly common on the SAT, and you need to be extra careful to turn them into the correct multiplication factor. For example, increasing something by 220% is the same as multiplying by 3.2.) Sometimes you need to work successive percents, or work a percent backwards, which can be confusing. If you are skilled at turning percent problems into multiplication problems, and then solving them algebraically, you shouldn't have much trouble here. Otherwise, you may want to focus some of your practice time on this category. Here are the easy, medium, and hard practice problems from the SAT Practice Problem Databank.

Statistics and Probability

These categories each make up a relatively small proportion of the practice problem databank, and, one would assume, a comparatively small proportion of actual tests. The last two categories have to do with fancy statistics, but they are quite tiny and not that difficult, especially if you have studied any statistics in your math classes.

One-Variable Data — The full title is One-variable data: Distributions and measures of center and spread. This category includes a few problems involving frequency tables, box plots, and bar graphs, but the vast majority of the problems in this category have to do with measures of center and spread, i.e. mean, median, and range. You might rarely have to answer a question about a standard deviation, but you'll never need to calculate one. All you need to remember is that larger standard deviations mean that the data is more spread out. Here are the easy, medium, and hard practice problems from the SAT Practice Problem Databank.

Two-Variable Data — The full title is Two-variable data: Models and scatterplots, and this category covers corrlations between two related measurements, usually represented in a graph or scatterplot. Here are the easy, medium, and hard practice problems from the SAT Practice Problem Databank.

Probability — This is not a large category, and many of the problems here simply involve constructing a probability fraction. You just have to figure out what to put in the numerator and what to put in the denominator. Here are the easy, medium, and hard practice problems from the SAT Practice Problem Databank.

Inference — The full title is Inference from sample statistics and margin of error. Some of the questions ask you to interpret results, and you can rule out any answers that include definitely or certainly. When drawing conclusions with statistics on the SAT, wishy-washy answers are better than absolute answers. With any question that involves margin of error, the correct answer is probably the one that says It is plausible that the measurement is between (value minus margin) and (value plus margin).. Here are the easy, medium, and hard practice problems from the SAT Practice Problem Databank.

Claims — The full title is Evaluating statistical claims: Observational studies and experiments, and questions in this category are extremely rare. Several of the questions revolve around recognizing the difference between a random sample and a biased sample. Here are the easy, medium, and hard practice problems from the SAT Practice Problem Databank.