Advanced Placement Preparation Statistics
PREREQUISITE: None
AVAILABILITY: Blyth Academy Online
Please Note: This is a preparation course only. A credit will not be issued by Blyth Academy Online. Students wishing to earn an Advanced Placement credit must write the official AP exam that is administered by the College Board.
The Advanced Placement Statistics course is equivalent to a one-semester, introductory, non-calculus-based college course in statistics. The course introduces students to the major concepts and tools for collecting, analyzing, and drawing conclusions from data. There are four themes in the AP Statistics course: exploring data, sampling and experimentation, anticipating patterns, and statistical inference. Students use technology, investigations, problem solving, and writing as they build conceptual understanding.
UNIT ONE
Introduction to Descriptive Statistics Essential Question: How can we construct and interpret graphical displays of single variable data distributions?
- In this unit, students will be exploring data. Students will learn to construct and interpret graphical displays of single variable data distributions. They will begin with a basic vocabulary overview, list different types of data and discuss several methods of displaying univariate data.
UNIT TWO
Describing Data Essential Question: How can we create 'picture' of the data to help us make decisions and interpret patterns?
- In this unit, students will explore different ways to display their data. A ‘picture’ of the data will help them to make decisions as to their next steps. Pictures may reveal things that are not immediately apparent when the data is listed in raw form. Students are able to spot patterns and shapes more readily in graphs. Pictures also allow them to describe the data to others.
UNIT THREE
Numerical Measures for Data Essential Question: What are the measures of location and dispersion?
- In this unit, students will discuss measures of location; arithmetic mean, weighted mean, median and mode, and be able to understand their characteristics. Students will also gain an understanding of the concepts of symmetry and skewness. Students will learn about measures of dispersion including range, mean deviation, standard deviation, variance and percentiles. Students will learn about the Empirical Rule and calculate the coefficients of variation and skewness.
UNIT FOUR
Bivariate Data Essential Question: How can the discussion of Bivariate Data help in understanding scatterplots, variables, and the method of least squares?
- In this unit, students will discuss Bivariate Data where we jointly consider two variables. Students will identify independent and dependent variables, learn how to prepare scatterplots and calculate the linear regression for a linear plot equation using the method of least squares.
UNIT FIVE
Probability and Random Variables Essential Question: How does the understanding of properties of probability make sense of inference?
- In this unit, students will learn the definition of probability including classical, empirical and subjective approaches to probability. Students will gain an understanding of mutually exclusive events, collectively exhaustive events, joint event, complementary events, dependent events and independent events. Students will learn how to calculate the number of outcomes or arrangements using basic counting principles. Students will also solve probability problems using the complementary rule, the addition rules, the multiplication rules, the conditional rule and contingency tables. Students will use Venn diagrams and probability trees to represent probability and solve problems.
UNIT SIX
Discrete Probability Distributions Essential Question: What do we mean by discrete probability distribution?
- In this unit, students will discuss discrete probability distributions. Students will learn how to define the terms random variable and probability distribution and distinguish between discrete and continuous probability distributions.
UNIT SEVEN
The Normal Probability Distribution Essential Question: What is the Normal Model and when do we use it?
- In this unit, students will gain an understanding of the characteristics of a normal distribution. Students will also calculate Z scores and probabilities associated with normal distributions.
UNIT EIGHT
Sampling Methods and the Central Limit Theorem Essential Question: Why is the Central Limit Theorem so important in studying statistics?
- In this unit, students will learn the need for sampling and gain an understanding of sampling error. Students will learn about the various sampling methods including simple random, stratified, systematic, cluster and convenience. Students will learn about the sampling distribution of the mean. Students will learn how to calculate the mean of the sampling distribution of the mean and the standard error of the mean. Students will also solve probability problems involving the Central Limit Theorem.
UNIT NINE
Confidence Intervals Essential Question: What is the confidence interval and why do we use it?
- In this unit, students will learn the definition of the terms estimation, point estimate, confidence level, confidence interval, and level of significance. Students will construct confidence intervals for the population mean using the `Z’ tables and learn about student t-distribution. Students will also construct confidence intervals for the population mean using the student t-table and will gain an understanding of when to use the Finite Population Correction Factor.
UNIT TEN
Hypothesis Testing Essential Question: When and how do we use Hypothesis tests?
- In this unit, students will learn the definition of a hypothesis and be learn how to state the null and alternate hypothesis. Students will learn about level of significance, critical value, test statistic, Type I and Type II Error. Students will perform two-tailed and one-tailed hypothesis tests for the population mean and population proportion using the `Z’ table and the student t-table. Students will also perform hypothesis tests for the difference between two means or two proportions.
CULMINATING ACTIVITY
- As students prepare now to write their University Statistics Exam, they will see the benefit of doing as many practice problems as they can. This culminating activity is the final task for this course, it will provide students with the opportunity to challenge their knowledge of concepts learned throughout this course.