Statistics

a number that describes a sample Ex: the mean height of students in 1st period AP Stats

parameter

a number that describes a population Ex: the mean height of all students at PHS

Statistics (capital “s”)

is the science and art of collecting, analyzing, and representing data

Individual

the object described in a set of data Ex: people, animals, things…

Variable

an attribute (characteristic) that can take on different values for different individuals Ex: height, age, weight, or scores on a test

Variable Types

Categorical and Quantitative

Categorical Variable

a variable that assigns labels to each individual and puts them in distinct groups, such as gender or eye color, without any distinct numerical value

Quantitative Variable

takes on numeric values that represent measurable quantities

Identifier

not all numbers are quantitative, some are identifiers like SSN and school lunch codes

Kinds of Quantitative Variables

Discrete and Continuous

Discrete Quantitative Variable

a variable that can take on a fixed set of specific values with gaps between, things that only go by certain measurement integers Ex. siblings, shoes size, and pets

bc you can’t have half a sibling

Continuous Quantitative Variable

a variable that can take on any value within a given range, often large decimals and fractions Ex: height, timed run, weight

distribution

the distribution of a variable tells us what values that variable can take and how often those values occur within a data set a.k.a the pattern of variation Ex: can be a table, graph, chart, or in words

Frequency Table

shows the number of individuals having each value of a variable in a dataset, often represented in a tabular format. It summarizes how often each value occurs.

Relative Frequency Table

shows the proportion or percent of individuals having each value of a variable in relation to the total number of observations in a dataset Ex: 2/10 people

bar chart

shows each category as a bar. The heights of the bars show the category frequencies or relative frequencies

pie chart

shows each category as a slice of “pie.” The areas of the slices are proportional to the category frequencies or relative frequencies

Area Principle

the area taken up by a bar on a graph should be proportional to the % of the population it represents

2-Way Table

displays distribution of two categorical variables

frequency

count in each cell (box) of the table, the number of times a single event or value occurs in a dataset

margins

the totals along the outside of the table

Two variables are associated if…

the probability of one event changes once we know the other has occurred

If variables are not associated, they are said to be…

independent from each other.

marginal relative frequency

gives the percent or proportion of individuals that have a specific value for one categorical variable

joint relative frequency

gives the percent or proportion of individuals that have a specific value for one categorical variable and a specific value for another categorical variable

conditional relative frequency

gives the percent or 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)