Mastering Problem-Solving and Data Analysis on the SAT

Dimensional Analysis

The process of keeping track of units during calculations to ensure proper conversions.

Rate

A ratio comparing two different units (e.g., miles per hour, dollars per pound).

Density

A specific type of rate defined as mass per unit volume (Density = m/v) or population per unit area.

Proportional Relationship

Two quantities, x and y, are directly proportional if y = kx, where k is the constant of proportionality.

Percent Increase

To increase a number x by p%, multiply by (1 + p/100).

Percent Decrease

To decrease a number x by p%, multiply by (1 - p/100).

Percent Change Formula

% Change = (New Value - Old Value) / Old Value × 100.

Mean

The average of a set of numbers calculated as the sum of data points divided by their count.

Median

The middle value in an ordered dataset; if even, the average of the two middle numbers.

Mode

The most frequently occurring value in a dataset.

Outlier

An extreme value that can skew data and affect statistical measures.

Standard Deviation (SD)

A measure of the average distance of data points from the mean.

Box Plot

A visual representation displaying the Five Number Summary: Min, Q1, Median, Q3, and Max.

Line of Best Fit

A linear equation used to model the trend in bivariate data, typically written as y = mx + b.

Residual

The difference between the actual data point and the predicted value from a model.

Linear Growth

A pattern of increase by a constant amount over time.

Exponential Growth

A pattern of increase by a constant percentage or factor over time.

Basic Probability Formula

P(Event) = Number of favorable outcomes / Total number of possible outcomes.

Conditional Probability

The probability of an event given a specific condition, restricting the denominator.

Population

The entire group you want to know about in a statistical study.

Sample

A subset of the population that is actually measured in a study.

Random Selection

The method of choosing participants randomly from a population to generalize results.

Margin of Error

The measure of uncertainty associated with a sample statistic; larger samples lead to lower margins of error.

Correlation

A relationship or association between two variables where one may predict the other.

Causation

A determination that one event (variable) directly causes another event (variable).

Unit Conversion

The process of converting a quantity from one unit of measurement to another.

Dimensional Cancellation

A technique in unit conversion where unwanted units are eliminated by proper arrangement of conversion factors.