# AP Statistics Course

## GK Consultants Statistics Course

### What does this course mean for you?

This course is ideal for budding mathematicians with a keen interest in data and statistics. You will learn everything that you need to know about collecting and analysing data, including drawing your own sound conclusions from the cyphered information. Perfect for those who are looking to pivot their career or try something entirely different.

### About our Statistics Course

In this statistics course you will begin to learn about the major concepts and tools that are used by statisticians who collect, analyse, and draw conclusions from data. Throughout this course you will explore statistics through discussion and various activities, including designing your own surveys and experiments.

### The skills you will gain

• Learn how to select the best methods for collecting or analysing data
• Gain the ability to describe patterns, trends, associations, and relationships in data
• You will be able to use probability and simulation in order to describe the probability distributions, and define uncertainty in statistical inference
• The ability to use statistical reasoning to draw the appropriate conclusions and justify your claims with evidence

### Course equivalency

• This course is the equivalent to a one-semester, introductory, non-calculus-based college course in statistics

### Recommended course prerequisites

• We recommend that you have completed a second-year course in algebra before starting this course

### About the Statistics Course Units

The course content listed below has been organised into the way in which it is most commonly taught in order to provide a clear sequence of comprehension throughout. However, your teacher may choose to present the course content differently. In either case, you will receive all of the information you need to gain a comprehensive understanding of statistics.

## Unit 1 – Exploring One-Variable Data

Starting in unit 1 you will be introduced to the way in which statisticians approach variation, and practice representing data, describing distributions of data, and drawing up sound conclusions based on clear theoretical distribution.

Topics include:

• Identifying variation in categorical and quantitative variables
• Learn how to represent data using tables or graphs
• Calculating and interpreting various statistics
• Exploring, describing, and comparing distributions of data
• What is the normal distribution?

This unit contributes 15%–23% of the final exam score.

## Unit 2 – Exploring Two-Variable Data

In unit 2 you will begin to build on what you’ve learned by representing two-variable data, descripting relationships between variables, comparing various distributions, and using a number of different models to make accurate predictions.

Topics include:

• Learn how to compare and represent 2 categorical variables
• Exploring the calculation of statistics for 2 categorical variables
• Learn how to represent bivariate quantitative data using scatter plots
• Learn how to define associations in bivariate data and interpreting correlation
• What are linear regression models?
• Define residuals and residual plots
• Exploring departures from linearity

This unit contributes 5%–7% of the final exam score.

## Unit 3 – Collecting Data

Next you will be introduced to study design. This includes the importance of randomisation. You will also begin to understand how to best interpret the results of optimally-designed studies and draw your own appropriate conclusions and generalisations.

Topics include:

• How to plan a study
• How to use sampling methods
• Identifying sources of bias in sampling methods
• Learn how to design an experiment
• How to effectively interpret the results of an experiment

This unit contributes 12%–15% of your final exam score.

## Unit 4 – Probability, Random Variables, and Probability Distributions

In unit 4 you will learn about the fundamentals of probability. Following that you will be introduced to the probability distributions that are the basis for statistical inference.

Topics include:

• Learn how to use simulation to estimate probabilities
• Learn how to calculate the probability of a random event
• Explore random variables and probability distributions
• What is the binomial distribution?
• What is the geometric distribution?

Unit 4 contributes 10%–20% of your final exam score.

## Unit 5 – Sampling Distributions

Next up you will build a deeper understanding of sampling distributions and lay the foundations for estimating characteristics of a population and quantifying with confidence.

Topics include:

• Understanding the variation in statistics for samples collected from the same population
• What is the central limit theorem?
• Explore biased and unbiased point estimates
• Understanding sampling distributions for sample proportions
• Understanding sampling distributions for sample means

This unit contributes 7%–12% of your final score.

## Unit 6 – Inference for Categorical Data: Proportions

Unit 6 involves inference procedures for proportions of categorical variables, and understanding statistical inference, which is a concept that you will continue to explore in greater depth as the units’ progress.

Topics include:

• Learn how to construct and interpret a confidence interval for a population proportion
• Set up and carry out a test for a population proportion
• Learn how to interpret a p-value and accurately justify a claim about a population proportion
• Define type I and Type II errors in significance testing
• Explore confidence intervals and tests for the difference of 2 proportions

Unit 6 contributes 12%–15% of your overall exam score.

## Unit 7 – Inference for Quantitative Data: Means

Unit 7 begins building on the lessons that you have learned previous on inference in Unit 6. You will then learn about how to analyse quantitative data to make inferences about various population means.

Topics include:

• How to construct and interpret a confidence interval for a population mean
• Learn about setting up and carrying out a test for a population mean
• Learn how to interpret a p-value and justify a claim about a population mean
• Explore confidence intervals and tests for the difference of 2 population means

This unit will contribute 10%–18% of your score.

## Unit 8 – Inference for Categorical Data: Chi-Square

Unit 8 is dedicated to learning about chi-square tests, which can be used when you are faced with two or more categorical variables.

Topics include:

• Explore the ‘chi-square’ test for goodness of fit
• Learn about the ‘chi-square’ test for homogeneity
• Define the ‘chi-square’ test for independence
• Learn how to select an appropriate inference procedure for categorical data

This unit contributes 2%–5% of your final exam score.

## Unit 9 – Inference for Quantitative Data: Slopes

In the 9th and final unit you will begin to understand that the slope of a regression model is not necessarily the true slope, but is based on a single sample of a sampling distribution. Using this information you can construct confidence intervals and begin to perform significance tests for this particular slope.

Topics include:

• What are confidence intervals for the slope of a regression model?
• How do you set up and carry out a test for the slope of a regression model?
• Learn how to select an appropriate inference procedure

This unit contributes 2%–5% of your final exam score.

### Conclusion

Upon completing this course you will have gained a thorough and comprehensive understanding of statistics, the way that they are accurately gathered, and how they can be used to draw a particular outcome. This is a college-equivalent qualification that will position you well to explore new career opportunities within the statistics industry and give you the confidence to get off to a strong start.