International Baccalaureate Mathematics

Syllabus Content

Concepts of population, sample, random sample, discrete and continuous data. Reliability of data sources and bias in sampling. Interpretation of outliers. Sampling techniques and their effectiveness

Here are some exam-style questions on this statement:

"Jimmy is ordering the t-shirts for the community choir which has 240 members." ... more

"The Student Council in a large school conducted a survey to find out how many classes assigned homework for students to complete." ... more

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Here is an Advanced Starter on this statement:

Ghosts or Papua New Guinea
A probability prediction based on a biased sample more

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Data Handling Data is talked about more this decade than ever before. Whether it be how social media companies deal with your personal data or how analysing data can improve algorithms for systems that make everyday life easier or more profitable. Pupils are first introduced to small, familiar data sets and learn to visualise them in many different ways. They may produce their own data from experiments, observations or games and will then describe their data in different ways. Pupils will calculate averages and other summary measures (mean, median, mode range) and produce bar charts, pie charts and box plots. Older pupils will use technology to help analyse larger data sets and will be introduced to inter-quartile range and standard deviation. They will draw conclusions from scatter diagrams, and have a basic understanding of correlation. They will learn how to apply statistical information to calculate probabilities. See also the topics called Statistics, Averages and Probability.

Live Data One of the big differences between Maths from a textbook and Maths from the web is the possibility of using live data. This possibility gives problem solving real context and allows investigating statistical connections to be far more meaningful.

Statistics Statistics is the study of the collection, organisation, analysis, interpretation and presentation of data. It deals with all aspects of data, including the planning of data collection in terms of the design of surveys and experiments. It also includes describing mathematical relationships between variables and presenting these to an audience in a way that best conveys meaning. See also the topics called Data Handling, Probability and Averages.

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Official Guidance, clarification and syllabus links:

This is designed to cover the key questions that students should ask when they see a data set/analysis.

Dealing with missing data, errors in the recording of data.

Outlier is defined as a data item which is more than 1.5 × interquartile range (IQR) from the nearest quartile.

Awareness that, in context, some outliers are a valid part of the sample but some outlying data items may be an error in the sample.

Link to: box and whisker diagrams (SL4.2) and measures of dispersion (SL4.3).

Simple random, convenience, systematic, quota and stratified sampling methods.

In statistics, the population refers to the entire set of items or individuals under study, while a sample is a subset chosen from this population. A random sample is a sample selected in a way that every member of the population has an equal chance of being included. Data can be categorised as discrete if it can only take specific values (e.g. the number of students in a class) and continuous if it can take any value within a range (e.g. height of a student). The reliability of data sources assesses the consistency and trustworthiness of the data. It's crucial to be aware of bias in sampling, as it can skew results and interpretations. Outliers are data points that significantly differ from the rest of the data and need careful interpretation. Various sampling techniques exist, each with its effectiveness, depending on the situation.

For example, consider a school with $ N $ students, and we want to calculate the average height. If we measure the height of every student, we are dealing with the population. However, if we measure only a subset (say 30 students randomly chosen), we are dealing with a sample. Suppose the heights of these 30 students are $ x_1, x_2, \dots, x_{30} $. The sample mean would be:

$$ \bar{x} = \frac{x_1 + x_2 + \dots + x_{30}}{30} $$

This sample mean can give us an estimate of the average height of all students in the school, but it may not be the exact population mean.

Sampling methods - aid memoire

Simple random sampling [GDC skill random integer]
Systematic sampling [Regular intervals]
Convenience sampling [Convenient for the experimenter]
Stratified/Quota sampling [Eg. School survey number from each YG proportional - randomly chosen]

Data Sampling Methods This video covers Data Sampling Methods and is from is from Revision Village

This video on outliers is from Revision Village and is aimed at students taking the IB Maths Standard level course

This Bicen Maths video clip shows everything you need to memorise on Data Collection and Sampling for A Level Statistics.

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International Baccalaureate Mathematics

Statistics and Probability

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