IBDP Mathematics Applications & Interpretations SL Chapter 3 Notes

Representing and describing data: descriptive statistics

STUDY NOTES FOR MATHEMATICS – CHAPTER 3 – Representing and describing data: descriptive statistics

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All DP mathematics courses serve to accommodate the diverse range of needs, interests and abilities of students, and to fulfill the requirements of various university and career aspirations. The aims of these courses are to enable students to: develop mathematical knowledge, concepts, principles, logical, critical and creative thinking, employ and refine their powers of abstraction and generalization. Students are also encouraged to appreciate the international dimensions of mathematics and the multiplicity of its cultural and historical perspectives.

In the other chapters we have studied discrete and continuous random variables and its properties. However, we have one considered one random variable at a time, which is quite unrealistic in the real world. For example, when we take a sample of measurements from a population, we must treat each measurement as a random variable. In statistics we formalise this idea by defining a random sample. In this chapter, we use the properties of random samples to explore the statistical theory behind estimation. We also consider bivariate data, which means data has two variables recorded for each individual. In most real-world situations, there will not be an exact relationship between the two variables. Our goal is to find which model best fits the data and measure how strong the relationship between the variables is. We delve into topics such as correlation when using scatter plots by drawing the line of best fit to classify the strength between variables. We also learn to depict data using histograms, box and whisker plots and cumulative frequency graphs as well.
We also use probability to model the random variation or distribution of numerical variables. We learn about the different types of variables such as random, discrete random and continuous random. For each of these variables, there is a corresponding probability distribution which describes the probability that the variable will take a particular value.