ap statistics semester one review part 2 chapters 4-6 semester one review part 2 chapters 4-6
TRANSCRIPT
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