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Titel
4
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Statistics
Topics Covered:
4.1 Concepts of population, sample, and random sampling
4.2 Presentation of data (frequency tables, histograms, cumulative frequency graphs)
4.3 Measures of central tendency (mean, median, mode) and spread (range, interquartile range, standard deviation)
4.4 Correlation and linear regression (scatterplots, Pearson’s correlation coefficient)
4.10 Interpretation of the parameters of a linear model
Learning Objectives
By the end of this unit, students will be able to:
Distinguish between populations and samples and understand basic sampling methods.
Represent data appropriately using tables, histograms, and cumulative frequency curves.
Calculate and interpret measures of central tendency and spread.
Analyze data using scatterplots, describe correlation, and use linear regression to model relationships.
Interpret the slope and intercept of linear models in context.
Content Overview
1. Populations and Samples (4.1)
Understanding populations, samples, and the purpose of sampling.
Different sampling techniques (random, stratified, etc.).
2. Data Presentation (4.2)
Frequency distributions, cumulative frequency tables.
Histograms and cumulative frequency graphs.
Boxplots and understanding quartiles and outliers.
3. Measures of Central Tendency and Spread (4.3)
Mean, median, mode, range, interquartile range (IQR), and standard deviation.
Interpreting and comparing data sets using these measures.
4. Correlation and Linear Regression (4.4)
Scatterplots and describing relationships between two variables.
Pearson’s correlation coefficient, interpretation of strength and direction.
Line of best fit by least squares method.
5. Interpretation of Linear Models (4.10)
Meaning of slope and intercept in real-world contexts.
Using models to predict values and understanding limitations.
Theory of Knowledge (TOK) Links
How do we decide whether data truly represents reality?
What is the role of context in interpreting statistics?
How do models influence our interpretation of data, and when might they mislead us?
To what extent can correlation imply causation, and what are the dangers of assuming it does?
Approaches to Learning (ATL) Skills
Research Skills: Gather and interpret data sets.
Thinking Skills: Critically assess the appropriateness of statistical models.
Communication Skills: Present data visually and explain findings in context.
Self-Management Skills: Organize and manage data-handling processes systematically.
Information Literacy: Evaluate and use secondary data sources appropriately.
Assessment Opportunities
Formative Assessment:
Quizzes on calculating and interpreting measures of center and spread.
Data presentation projects (e.g., creating histograms, boxplots).
Small group data investigations and presentations.
Summative Assessment:
Unit test including both theoretical questions and practical applications (interpretation of regression outputs).
Data investigation task using technology (e.g., spreadsheet software or a GDC).
Resources
IB Mathematics: Analysis and Approaches SL textbook
Graphical Display Calculator (GDC)
Online tools: Desmos, GeoGebra Statistics Tool
IB Question Bank for past paper practice
Interdisciplinary Connections
Economics: Analyzing economic data trends.
Biology: Modeling population growth or environmental data.
Social Sciences: Interpreting survey data and trends.
Differentiation Strategies
For students needing support:
Step-by-step scaffolded practice on calculating statistics and constructing graphs.
Use real-life datasets that are more relatable or less complex.
For advanced learners:
Explore non-linear models briefly for comparison.
Investigate real-world datasets with multiple variables (introducing the idea of multiple regression informally).
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