AP Stats Unit 2

Two Way Table/Contingency Table

A table of counts describing two categorical variables

Joint Relative frequency

An individual cell frequency divided by the table total

For example: 45/150

Marginal relative frequency

A proportion describing a category from one variable (one table margin)

Calculated by dividing a column or row total by table total

For example: 70/150

Side by Side Charts

Allows you to compare the frequencies or relative frequencies of categories between two groups

Conditional Relative Frequency

A proportion of a subgroup that meets a certain condition

Calculated by dividing an individual cell by a row total or column total

For example: 30/75

Segmented Bar Charts & Mosaic Plots

1. Compare proportions or percentages between groups

2. See how the distribution of one variable changes depending on the other

3. Identify patterns and differences among categories

Describing Associations

1. Make a claim (there is/isn’t an association)

2. Support by comparing percentages between groups

3. Include context (mention variables)

Sample Space

Set of all possible outcomes

Event

A collection of outcomes

Probability formula

Probability = # of outcomes in an event/# of total possible outcomes

Probability

The relative frequency of an out come after many trials

Probabilities are between 01

P(R)+ P(B) = 1

Law of large numbers

After many trials, the relative frequency of outcomes will approach their probability

Simulation with replacement

Adding back a possibility.

For example: Picking out a marble and putting it back

Simulation without replacement

Taking away a possibility.

For example: Picking out a marble and leaving it out

The probability of an Event Not Happening Equation

(P(E)+P(E^c)=1

Ven diagrams

Upside Down (U): And

C: Probability of event … not occurring

Upper Case (U): Or

Mutually Exclusive Events/Disjoint events

When events cannot occur at the same time.

Condition

A “given” in a problem

Conditional Probability Formula

Probability that … will occur given that … has already occurred

Multiplication Rule Formula

Before going straight to the formulas, first try solving using you reasoning skills and the Keys to Probability

Keys to Probability

1. Draw it first

2. Divide by givens

3. Multiply by the ‘ands’

4. Add the ‘ors’

Tree Diagrams

Show all possible outcomes of events

Calculate the probability of different outcomes

Independence

Two events (A&B) are independent if knowing the outcome of one event does not affect the probability of the other event

Addition Rule Formula

Associtation

Two variables are related

Association does not mean CAUSATION

Causation

One variable directly causes a change in another