Stats & Prob
Statistics & Probability is topic #5 for Math SL and HL. Although the syllabus content for statistics and probability is packaged into one syllabus topic, in terms of organizing the material for teaching purposes it is sensible to divide the topic into smaller sub-topics or categories. In figuring out the best way to do this it is very important to recognize that a portion of the syllabus content in the SL Statistics & Probability topic is not included in the HL Statistics & Probability topic. Linear correlation of bivariate data is only in SL. I suggest the most plausible way to do this is to separate the content in this topic into three teaching units as follows:
1. Descriptive Statistics
2. General Probability
3. Probability Distributions
It can be argued quite strongly that statistics is the area of mathematics which has the greatest influence on our modern lives. Its applications are embedded in a wide range of industries that rely heavily on the information provided by statistical methods and concepts. How statistics works in our lives is sometimes very clear to see (e.g. election polls, sports, scientific research), but also there are many uses of statistics which are not as well known (e.g. insurance policies and costs, weather forecasting, airplane travel) but just as significant.
In terms of academic study - students pursuing an IB Diploma or a university degree - a basic understanding of statistics with some critical knowledge of how to apply some statistical techniques is critical. Students studying and doing research in virtually any academic subject will need to apply some statistical methods. It will be very helpful for students to understand the fundamentals behind these methods in order to help them make informed decisions on what methods to use and whether or not reasonable conclusions can be made from the statistical methods carried out. A student wishing to study any science or technical area at university - or pursue a master's degree or PhD - will certainly need to have a sufficiently thorough understanding of statistics and probability distribtions.
content on test: tree diagrams; conditional probability; probability distributions for discrete random variables continuous random variables; expected value (mean), variance & standard deviation for discrete & continuous data, binomial distribution, and Poisson distribution; normal distribution; standardization of normal variables; inverse normal distribution (worked solutions below)
worked solutions for the HL probability test above