A레벨_Mathematics(AS)_Statistics 1 > A레벨_AS
Statistics 1 introduces us to the common measurements we take in statistical situations, along with an introduction to probability theory.
Chapter 1 - Mathematical Modelling
We are introduced to the basic concept of a mathematical model, and how they are used to simplify real world problems and used to create predictions. A seven stage process for creating and refining a model is given.
Chapter 2 - Measures of Location and Spread
Different types of data must be treated differently, and the different types are introduced here. We then look at measures of location, such as the mean, median and mode, and measure of spread such as the interquartile range and standard deviation. We learn the various methods of estimating these depending on the data, and how they can be used to compare and contrast data-sets.
Chapter 3 - Representations of Data
In this chapter we take the data and statistics we found in the previous chapter and look at the different ways we can represent them visually. This includes the drawing of histograms and box-plots. We also look at identifying outliers, and determining whether or not a data-set is skewed.
Chapter 4 - Probability
The ideas of theoretical and experimental probability are first introduced, and we learn the notation of sets and its applications to probability. We see how to represent probability spaces via Venn-diagrams and tree diagrams. Definitions of independence and mutual exclusivity are given, and the concept of a conditional probability is presented.
Chapter 5 - Correlation and Regression
To determine the relationship between two variables, we can draw scatter diagrams and lines of best fit. Instead of guessing, we can use summary statistics to calculate an exact least squares linear regression line and the product moment correlation coefficient to see the strength of correlation. Using simple linear coding we can simplify our calculations.
Chapter 6 - Discrete Random Variables
In this chapter we begin introducing a formal framework for random variables and probability distributions. We look at the rules governing such distributions, including finding cumulative distributions, expectations and variances. Again we see how we can apply simple coding to distributions to aid problem solving.
Chapter 7 - The Normal Distribution
This final chapter introduces a ubiquitous distribution whose applications are common all over the world of science and economics. We look at how to standardise a normal distribution and use the cumulative distribution tables to find probabilities. We also see how to use the tables in reverse to find key values and the mean and standard deviation.
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