AP Statistics Unit 1: Exploring One-Variable Data

Vocabulary and formulas for Unit 1 of AP Statistics, covering data types, graphical representations, and numerical summaries of one-variable data.

Variable

Any characteristic that changes or varies from one individual or object to another.

Categorical Variable

A variable that places an individual into a category, group, or label.

Quantitative Variable

A variable that takes numerical values where arithmetic operations like finding an average make sense, such as height, salary, or temperature.

Discrete Variable

A quantitative variable that takes on a countable number of distinct values with gaps between them, such as shoe size or number of siblings.

Continuous Variable

A quantitative variable that can take any value within an interval or range; it is measured rather than counted, such as time, weight, or precise distance.

Frequency Table

A table that displays the count (frequency) of observations falling into each distinct category.

Relative Frequency Table

A table that shows the proportion or percentage of observations falling into each category, calculated by dividing the category count by the total number of observations.

Bar Chart/Bar Graph

A visual display for categorical data where the heights or lengths of separated bars represent frequencies or relative frequencies; bars do not touch.

Pie Chart

A circle divided into sectors, where each sector's area is proportional to the relative frequency of that specific category.

Dotplot

A simple graph where each data value is represented as a dot plotted above its respective location on a continuous number line.

Stem-and-Leaf Plot (Stemplot)

A display where quantitative data points are split into a 'stem' (leading digits) and a 'leaf' (the final digit); it must always include a key.

Histogram

A graph that groups quantitative data into continuous intervals called bins or classes of equal width; bars touch to depict continuity.

SOCV Framework

A framework for describing distributions of quantitative data addressing Shape, Outliers, Center, and Variability (or Spread).

Symmetric

A distribution where the left and right sides of the graph are roughly mirror images.

Skewed Right

A distribution where the tail of the graph extends further to the higher values (right side) and the mean is typically greater than the median.

Skewed Left (Negatively Skewed)

A distribution where the tail of the graph extends further to the lower values (left side) and the mean is typically less than the median.

Unimodal / Bimodal / Multimodal

Terms for a distribution having one, two, or multiple distinct peaks.

Uniform

A distribution where all outcomes are roughly the same frequency, making the graph relatively flat

Outlier

An extreme value that falls far outside the overall pattern of the rest of the data, confirmed mathematically using the $1.5 \times IQR$ rule.

Gaps/Clusters

Noticeable spaces where no data points exist, or strong groupings of data separated by gaps.

Mean ($\bar{x}$ or $\mu$)

The arithmetic average of a data set; it is highly sensitive to extreme values and is not resistant.

Median

The middle value when data points are arranged in ascending order; it is resistant to outliers.

Range

A single value calculated as the maximum value minus the minimum value ($\text{Max}$ - $\text{Min}$).

Interquartile Range (IQR)

The distance between the first and third quartiles ($Q3 - Q1$), representing the middle $50\%$ of the data; it is resistant to outliers.

Standard Deviation ($s$ or $\sigma$)

A measure of the typical or average distance of the data values from their mean.

Five-Number Summary

A structured summary consisting of the Minimum, First Quartile ($Q1$), Median, Third Quartile ($Q3$), and Maximum.

Boxplot (Box-and-Whisker Plot)

A visual representation of the five-number summary; modified versions show outliers explicitly as isolated points.

Percentile

The value such that $p$ percent of the observations fall at or below it.

Z-Score (Standardized Score)

The number of standard deviations a specific raw score falls above or below the mean, allowing for comparisons between different distributions.

Z-Score Formula

$$Z = \frac{x - \text{mean}}{\text{standard\_deviation}}$$

Lower Outlier Threshold

Q1−(1.5×IQR)

Upper Outlier Threshold

$$Q3 + (1.5 \times IQR)$$