AP Statistics - Chapter 1

Study guide for Chapters 1 and 2 of AP Statistics.

statistics

The science and art of collecting, analyzing, and drawing conclusions from data.

individual

An object described in a set of data, such as a person, animal, or thing.

variable

An attribute that can have different values for different individuals.

categorical

A variable that assigns labels that place an individual into a particular group.

quantitative

A number variable.

discrete

A quantitative variable that has a fixed set of possible values, such as the set of integers.

continuous

A quantitative variable that can refer to any real number.

distribution

Describes what values the variable takes and how often.

bar graph

Unordered graph with bars that represent categorical data.

dot plot

Ordered graph that can represent quantitative data using dots above a number line.

descriptive statistics

The process of exploratory data analysis.

inferential statistics

The process of drawing conclusions that go beyond the data at hand.

frequency

The number of times an event happens.

relative frequency

The number of times an event happens divided by the total.

proportion

A probability expressed as a number between 0 and 1.

percent

A probability expressed as a number between 0 and 100.

two-way table

A table of frequencies that summarizes the relationship between two categorical variables.

marginal relative frequency

The proportion of individuals that have a specific value for one categorical variable. It is the marginal divided by the total.

joint relative frequency

The proportion of individuals that have a specific value for one categorical and another categorical variable. It is the frequency divided by the total.

conditional relative frequency

The proportion of individuals that have a specific value for one categorical variable among individuals who share the same value of another categorical variable (the condition). It is the frequency divided by the condition’s total.

condition

The categorical variable used as the total for a conditional relative frequency.

conditional distribution

The distribution within a specific condition.

side-by-side bar graph

A graph that displays the distribution for a categorical variable for each value of another categorical variable. The bars are displayed side-by-side.

segmented bar graph

A graph that displays the distribution for a categorical variable as segments of a rectangle with the area being proportional to the frequency.

mosaic graph

A modified segmented bar graph in which the width of each rectangle is proportional to one category and the height is proportional to another category.

association

When knowing the value of one variable helps us know the value of another variable.

shape

A characteristic of a distribution that describes the symmetry, skew, and peaks of the distribution.

uniform

A distribution with the same probability throughout.

outlier

Any clear departure from the overall pattern.

Center

A measure of the middle of a distribution.

stemplot

Shows each data value as a stem that consists of all but the final digit and a leaf, containing all of the final digits for its stem.

histogram

A graph that shows each interval of values as a bar, with each bar being an equal width.

mean

The average of all the individual data values.

statistic

A number that describes some characteristic of a sample.

parameter

A number that describes some characteristic of a population.

resistant

When a statistical measure isn’t sensitive to outliers.

median

The midpoint of a distribution, such that half of the values are smaller and half are larger.

symmetric

When a distribution’s mean and median are approximately equal.

skewed left

When the mean is less than the median.

skewed right

When the mean is greater than the median.

range

The distance between the minimum and maximum.

standard deviation

The typical distance of the values in a distribution from the mean.

deviation

value - mean

sample variance

The sum of the square of all deviations, divided by n-1.

sample standard deviation

The square root of the sample variance.

quartiles

Divide ordered data into four groups having approximately the same number of values.

interquartile range

The distance between the first and third quartiles.

five number summary

The minimum, the first quartile, the median, the third quartile, and the maximum.

boxplot

A visual representation of a five number summary, containing a box from the first to the third quartile, a line at the median, and two whiskers going to the minimum and the maximum.

1.5xIQR rule

A common rule for finding outliers by trimming values that are 1.5 times the interquartile range greater than the third quartile or 1.5 times the interquartile range less than the first quartile.