AP Statistics Unit 1 Notes: Learning to Summarize One-Variable Data

Variation

The natural differences in data values from individual to individual; the reason graphs and summaries are useful.

Variable

A characteristic recorded for each individual in a dataset (e.g., height, eye color, minutes exercised).

Categorical variable

A variable that places individuals into groups; values are labels (e.g., political party, yes/no, brand).

Quantitative variable

A variable that takes numerical values for which arithmetic makes sense in context (e.g., height, reaction time, test score).

Distribution

What values a variable takes and how often it takes them.

Count (frequency)

The number of observations in a category (categorical data) or in a bin/interval (quantitative data).

Proportion (relative frequency)

A count divided by the total number of observations; often expressed as a percent.

Bar chart

A graph for categorical variables showing categories on one axis and counts/proportions on the other; bars are separated.

Dotplot

A quantitative graph that places a dot for each data value above a number line; repeated values stack.

Stemplot (stem-and-leaf plot)

A quantitative display that splits values into stems and leaves, preserving the original data values.

Stem (in a stemplot)

The leading digit(s) of each number used to group data values in a stem-and-leaf plot.

Leaf (in a stemplot)

The trailing digit of each number written next to the appropriate stem in a stem-and-leaf plot.

Key (stemplot key)

A note that explains the scale of a stemplot (e.g., 4|7 means 47).

Histogram

A quantitative graph that groups data into bins (intervals) and shows frequency in each bin; bars touch because the x-axis is a number line.

Bin (class interval)

A range of values used to group quantitative data in a histogram.

Relative frequency histogram

A histogram that uses proportions/percents (not counts) on the y-axis; useful for comparing groups with different sample sizes.

SOCS

A framework for describing quantitative distributions: Shape, Outliers (and other unusual features), Center, Spread.

Shape

The overall form of a quantitative distribution (e.g., symmetric or skewed; unimodal or bimodal).

Outlier

An observation unusually far from the rest of the data; can strongly affect mean and standard deviation.

Mean (x̄)

The arithmetic average of quantitative data: x̄ = (1/n)∑xᵢ; not resistant to outliers.

Median

The middle value of ordered data (or the average of the two middle values if n is even); resistant to outliers.

Range

A simple measure of spread: max − min; very sensitive to outliers.

Interquartile range (IQR)

A resistant measure of spread for the middle 50%: IQR = Q3 − Q1.

Standard deviation (s)

Measures a typical distance of values from the mean: s = sqrt[(1/(n−1))∑(xᵢ − x̄)²]; not resistant to outliers.

Resistant (statistic)

A statistic that is not strongly affected by extreme values (e.g., median and IQR are resistant; mean and standard deviation are not).