# Statistics S3

When studying pure mathematics at AS and A2 level you will be extending your knowledge of such topics as algebra and trigonometry as well as learning some brand new ideas such as calculus. While many of the ideas you will meet in pure mathematics are interesting in their own right, they also serve as an important foundation for other branches of mathematics, especially mechanics and statistics.

### Unit Content

1. Chapter 1 Combinations of Random Variables (S3) In this session, you will learn about Combinations of Random Variables, one of the 5 topics you need to be knowledgeable in to master the Unit S3 paper. After completing this session, you will be able to combine independent normal random variables and combine linear combinations of independent normal random variables.
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2. Chapter 2 Sampling (S3) In this session, you will learn about Sampling, one of the 5 topics you need to be knowledgeable in to master the Unit S3 paper. After completing this session, you will be able to take a simple random sample, use random numbers for sampling, take a stratified sample, take a systematic sample, take a quota sample, know the circumstances in which each method of sampling might be used, as well as know the advantages and disadvantages of the different methods of sampling.
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3. Chapter 3 Estimation, Confidence Intervals and Tests (S3) In this session, you will learn about Estimation, Confidence Intervals and Tests, one of the 5 topics you need to be knowledgeable in to master the Unit S3 paper. After completing this session, you will be able to understand the concept of an unbiased estimate, appreciate the significance of the Central Limit Theorem, know how to find confidence intervals for the population mean $$\mu$$.
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4. Chapter 4 Goodness of Fit and Contingency Tables (S3) In this session, you will learn about Goodness of Fit and Contingency Tables, one of the 5 topics you need to be knowledgeable in to master the Unit S3 paper. After completing this session, you will be able to form hypotheses about how well a distribution fits as a model for an observed frequency distribution, calculate the measure of goodness of fit, understand what is meant by degrees of freedom, work out the number of degrees of freedom, know the chi-squared $$(x^2)$$ family of distributions and be able to select the appropriate distribution, apply goodness of fit tests for the discrete distributions, including the discrete uniform, binomial and Poisson distributions, apply goodness of fit tests for the continuous distributions including the continuous uniform and Normal distributions, know what is meant by a contingency table, as well as apply goodness of fit to contingency tables.
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5. Chapter 5 Regression and Correlation (S3) In this session, you will learn about Regression and Correlation, one of the 5 topics you need to be knowledgeable in to master the Unit S3 paper. After completing this session, you will be able to calculate Spearman's rank correlation coefficient, calculate Spearman's rank correlation coefficient when there are no ties by using the easy formula, test the hypothesis that a product moment correlation coefficient is zero, as well as test the hypothesis that Spearman's rank correlation coefficient is zero.
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### Prerequisites and Requirements

Students who have achieved a grade of 'C' or higher in their IGCSE, GCSE, or any other equivalent 'O' Level Mathematics.

### What's Next?

Core Mathematics
C12
Edexcel International A Level Mathematics