PSAT 10 Math — Problem-Solving & Data Analysis Study Notes

Ratio

A comparison of two quantities by division.

Equivalent Ratios

Ratios that represent the same multiplicative comparison.

Unit Rate

A rate that compares a quantity to one unit of another quantity.

Constant of Proportionality

The constant factor in a proportional relationship.

Dimensional Analysis

A method of converting between units by treating them like factors that can be canceled.

Percent

A ratio that compares a number to 100.

Percent Increase

A calculation of how much a quantity has increased relative to its original value.

Percent Decrease

A calculation of how much a quantity has decreased relative to its original value.

Mean

The average of a set of values, calculated by dividing the sum by the number of values.

Median

The middle value in a list of numbers when arranged in order.

Interquartile Range (IQR)

The difference between the third quartile (Q3) and the first quartile (Q1) in a data set.

Scatterplot

A graph that displays values for two variables as points on a coordinate plane.

Linear Model

A mathematical representation of the relationship between two variables as a straight line.

Residual

The difference between the actual value and the predicted value in a regression model.

Probability

The measure of the likelihood that an event will occur.

Independence (in probabilities)

Two events are independent if the occurrence of one does not affect the occurrence of the other.

Margin of Error (MOE)

An expression of the amount of random sampling error in a survey's results.

Sampling Bias

A type of bias that occurs when the sample collected is not representative of the population.

Causation

A relationship in which one variable directly affects another variable.

Observation Study

A study where individuals are observed without interference from the researcher.

Hypothesis Testing

A statistical method used to make decisions about the parameters of a population based on the data obtained from a sample.

Confounding Variables

Variables that the researcher failed to control or eliminate, damaging the internal validity of an experiment.

Frequency Distribution

A summary of how often each value occurs in a dataset.

Two-Way Table

A table that displays the frequency distribution of two categorical variables.

Proportional Relationship

A relationship where two quantities increase at the same rate, represented mathematically as $y=kx$.

Box Plot

A graphical representation that displays the five-number summary of a dataset.

Percent of a Quantity

Calculated by multiplying the quantity by the decimal equivalent of the percent.