AP StatisticsAP StatisticsSemester One

ReviewPart 2

Chapters 4-6

Semester OneReviewPart 2

Chapters 4-6

AP Statistics Topics

Describing Data

Producing Data

Probability

Statistical Inference

Chapter 4: Designing

Studies

Chapter 4: Designing

StudiesIn this chapter, we

learned methods for collecting data through

sampling and experimental design.

In this chapter, we learned methods for

collecting data through sampling and

experimental design.

Sampling Design

Our goal in statistics is often to answer a question about a population using information from a sample.

to do this, the sample must be representative of the population in question

Observational Study vs. Experiment

SamplingIf you are performing an observational study, your sample can be obtained in a number of ways:

Convenience Sample

Simple Random Sample

Stratified Random Sample

Systematic Random Sample

Cluster Sample

Experimental DesignIn an experiment, we impose a treatment with the hopes of establishing a causal relationship.

3 Principles of Experimental Design

Randomization

Control

Replication

Experimental DesignsExperiments can take a number of different forms:

Completely Randomized Design

Randomized Block Design

Matched Pairs Design

Chapter 5: Probability:

What are the Chances?

Chapter 5: Probability:

What are the Chances?

This chapter introduced us to the basic ideas behind

probability and the study of randomness.

We learned how to calculate and interpret the probability

of events in a number of different situations.

This chapter introduced us to the basic ideas behind

probability and the study of randomness.

We learned how to calculate and interpret the probability

of events in a number of different situations.

ProbabilityProbability is a measurement of the likelihood of an event. It represents the proportion of times we’d expect to see an outcome in a long series of repetitions.

Probability Rules

0 ≤ P(A) ≤ 1

P(SampleSpace) = 1

P(AC) = 1 - P(A)

P(A or B) = P(A) + P(B) - P(A and B)

P(A and B) = P(A) P(B|A)

A and B are independent if and only if P(B) = P(B|A)

The following facts/formulas are helpful in calculating and interpreting the probability of an event:

Strategies

When calculating probabilities, it helps to consider the Sample Space.

List all outcomes, if possible

Draw a tree diagram or Venn diagram

Sometimes it is easier to use common sense rather than memorizing formulas!

Chapter 6: Random Variables

Chapter 6: Random Variables

This chapter introduced us to the concept of a random

variable.We learned how to

describe an expected value and variability of

both discrete and continuous random

variables.

This chapter introduced us to the concept of a random

variable.We learned how to

describe an expected value and variability of

both discrete and continuous random

variables.

Random VariableA Random Variable, X, is a variable whose outcome is unpredictable in the short-term, but shows a predictable pattern in the long run.

Discrete vs. Continuous

Expected Value

The Expected Value, E(X) = µ, is the long-term average value of a Random Variable

E(X) for a Discrete X

VarianceThe Variance, Var(X) = σ2, is the amount of variability from µ that we expect to see in X.

The Standard Deviation of X,

Var(X) for a Discrete X

Rules for Means and Variances

The following rules are helpful when working with Random Variables.

Linear Transformations on Random Variables

Sums & Differences of Random Variables

Binomial SettingSome Random Variables are the result of events that have only two outcomes (success and failure). We define a Binomial Setting to have the following features:

Binary Situations (Two Outcomes - success/failure)

Independent trials

Number of trials is fixed - n

Probability of success is equal for each trial

Binomial ProbabilitiesIf X is B(n,p), the following formulas can be used to calculate the probabilities of events in X.

The mean and standard deviation of a binomial distribution simplifies to the following formulas:

Geometric SettingSome Random Variables are the result of events that have only two outcomes (success and failure), but have no fixed number of trials. We define a Geometric Setting to have the following features:

Binary Situations (Two Outcomes - success/failure)

Independent trials

Trials continue until a success occurs

Probability of success is equal for each trial

Geometric ProbabilitiesIf X is Geometric, the following formulas can

be used to calculate the probabilities of events in X.

The mean of a geometric distribution simplifies to the following formula:

Semester One Final Exam

Semester One Final Exam

50 QuestionsMultiple Choice

Chapters 1-6

Tuesday and Wednesday

50 QuestionsMultiple Choice

Chapters 1-6

Tuesday and Wednesday