AP Stats Chapter 1

Two-way Table

Table summarizing relationship between 2 categorical variables

Marginal Relative Frequency

Percentage/proportion of individuals with specific value for 1 categorical variable

Joint Relative Frequency

Percentage/proportion of individuals with specific value for another categorical variable

Conditional Relative Frequency

Percentage/proportion of individuals with specific value for one variable given another variable

Conditional Distribution

Distribution of one variable given another variable

Association

Relationship between variables where knowing one helps predict the other

Individual

object described in a set of data (people, animals, things)

Variable

attribute that can take different values for different individuals

Categorical Variable

assigns labels that place each individual into a particular group, called a category

Quantitative Variable

Data that is in numbers (counts, measurements)

Distribution

tells us what values the variable takes and how often it takes those values

Histogram

shows each interval of values as a bar

Formula for low outliers

Low outliers < Q₁-1.5(IQR)

Formula for high outliers

High outliers > Q₃ + 1.5(IQR)

Mean: distribution of quantitative data is the avg of all individual data values

x-bar (x w/ a line above it)

Resistance

A statistical measure is resistant if it isn’t sensitive to extreme values

Range

distance between min & max value (max-min)

Standard deviation

measures typical distance of values in a distribution from the mean

S(subx) =

√ ∑ (x(subi) - x-bar) ² /n-1

Quartile

divides ordered data into 4 groups having roughly the same # of values

How to find quartiles

Arrange data values from smallest to largest & find the median

Q₁

median of the data values that are to the left of the median in the ordered list

Q₃

median of the data values that are to the right of the median in the ordered list

IQR

distance between the 1st & 3rd quartiles of a distribution

Q₃-Q₁

5 number summary

{ min, Q₁ , median, Q₃, max}

Boxplot

visual representation of five-number summary

Variance

value obtained before taking the square root in the standard deviation calculation

What should you mention when asked to describe the distribution of a quantitative variable?

shape, center, variability, outliers

Frequency table

shows number of individuals having each value

Relative frequency table

show proportion or % of individuals having each value