AP Statistics — Exploring & Describing Data

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Categorical vs. Quantitative Variables

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Categorical variables place individuals into groups (e.g., eye color), while quantitative variables take numerical values that represent quantities (e.g., height). Quantitative data allows for arithmetic operations like averaging, whereas categorical data does not.

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Discrete vs. Continuous Variables

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Discrete variables can take on a countable set of possible values (often integers), such as the number of pets. Continuous variables can take any value in an interval on the number line, such as height or time, where precision depends on the measurement tool.

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SOCS (Describing Distributions)

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A framework for describing the distribution of a quantitative variable: Shape (symmetric/skewed), Outliers (unusual values), Center (mean/median), and Spread (range/IQR/SD). Always contextualize your answer in the specific scenario of the problem.

Front

Skewness and Center

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In a symmetric distribution, the mean and median are approximately equal. In a left-skewed distribution (tail left), the mean is pulled less than the median. In a right-skewed distribution (tail right), the mean is pulled greater than the median.

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Relative Frequency

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The proportion or percentage of data that falls into a specific category or class interval. It is calculated by dividing the frequency of the class by the total number of observations. Relative frequencies allow for comparison between datasets of different sizes.