AP Statistics Unit 1: Exploring One-Variable Data

Individual

The objects described by a set of data (e.g., people, animals, things).

Variable

Any characteristic of an individual that can take different values for different individuals.

Distribution

Tells us what values a variable takes and how often it takes these values.

Categorical Variable

Places an individual into one of several groups or categories.

Quantitative Variable

Takes numerical values for which it makes sense to find an average.

Discrete Quantitative

A quantitative variable that can only take a countable number of values (usually integers).

Continuous Quantitative

A quantitative variable that can take any value within an interval.

Frequency Table

Counts of individuals per category in categorical data.

Relative Frequency Table

Shows percent of individuals per category in categorical data.

Bar Chart

Represents each category as a bar with heights indicating frequency or relative frequency.

Dotplot

A simple graph where each data value is shown as a dot above its location on a number line.

Stemplot

Separates each observation into a stem (all but the final digit) and a leaf (the final digit).

Key (in Stemplots)

Explanation of what the stem and leaf represent in a stemplot.

Histogram

Used for larger datasets, divides data into classes (bins) of equal width with no spaces between bars.

SOCS

An acronym for describing distributions: Shape, Outliers, Center, and Spread.

Shape (in distribution)

Describes the overall pattern of the graph (e.g., symmetric, skewed).

Skewed Right

The right side (tail) is much longer than the left, indicating a tail points to the right.

Skewed Left

The left side (tail) is much longer than the right, indicating a tail points to the left.

Outlier

An unusual value that falls outside the overall pattern of the data.

Center (in distribution)

Describes the middle of the distribution, often using median or mean.

Spread (in distribution)

Describes how much variation is in the data, using range, IQR, or standard deviation.

Interquartile Range (IQR)

The range of the middle 50% of data, calculated as Q3 - Q1.

Standard Deviation ($s_x$)

The average distance of data points from the mean.

Comparative Language

Necessary language for comparing distributions, using terms like greater than, less than.

Bad Comparison

Listing statistics separately for groups without comparative language.

Common Mistakes in Statistics

Confusions between categorical and quantitative variables, or misinterpretation of graphs.