PSAT 8/9 Math — Problem-Solving and Data Analysis (Deep-Dive Study Notes)

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Last updated 12:33 PM on 8/7/26
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28 Terms

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Ratio

A comparison of two quantities by division.

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Rate

A ratio that compares quantities with different units.

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Unit Rate

A rate expressed per one unit, making comparisons easier.

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Proportional Relationship

When two quantities scale together at a constant multiplicative rate.

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Constant of Proportionality

The constant value (k) that relates two proportional quantities.

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Cross Multiplying

A method used to solve proportions by multiplying across the equal sign.

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Dimensional Analysis

A method to convert units by treating them as factors that can cancel.

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Percent

A ratio that compares a quantity to 100.

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Percentage Points

The unit for the difference between two percentages.

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Mean

The arithmetic average of a set of values.

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Median

The middle value when a data set is ordered.

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Mode

The most frequently occurring value in a data set.

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Range

The difference between the maximum and minimum values in a data set.

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Interquartile Range (IQR)

The spread of the middle 50% of a data set.

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Scatterplot

A graph that displays two-variable data; each point represents a pair of values.

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Correlation

A measure of the relationship between two variables.

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Residual

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

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Probability

A measure of the likelihood that an event will occur.

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Complement of Event

The event that encompasses all outcomes not in the specified event.

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Independent Events

Two events where the outcome of one does not affect the other.

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Dependent Events

Two events where the outcome of one affects the probability of the other.

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Conditional Probability

The probability of an event occurring given that another event has already occurred.

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Multiplication Rule

A rule to find the probability of two events occurring together.

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Theoretical Probability

Probability calculated based on reasoning or models, assuming all outcomes are equally likely.

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Experimental Probability

Probability calculated based on the results of an experiment or trial.

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Two-Way Table

A table that displays the frequency of different combinations of two categorical variables.

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Interpolation

Predicting a value within the range of known data.

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Extrapolation

Predicting a value outside the range of known data.