IB Maths AI Topic 4 Notes

This page contains our IB Maths AI notes for topic 4. By reading each one of these notes, you will fully cover the content for IB Maths AI 'Stats & Probability'.

All Topic 4 Sub-topics 4.1: Fundamentals Of Statistics 4.2: Visualising Statistics 4.3: Distribution Properties 4.4: Introduction To Linear Statistics 4.5: Probability 4.6: Probability Distributions 4.7: Hypotheses & Tests (HL)4.8: Data collection & categorisation (HL)4.9: Advanced linear statistics (HL)4.10: Linear transformations & combinations (HL)4.11: Confidence intervals (HL)4.12: Poisson distribution (HL)4.13: Distribution tests (HL)4.14: Transition matrices

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Chapters

4.1: Fundamentals of statistics

1. Populations & samples

2. Types of data

3. Reliability, bias & sampling

4. Frequency distributions

5. Measures of central tendency

6. Quartiles, spread & outliers

4.2: Visualising statistics

1. Histograms

2. Cumulative frequency tables & graphs

3. Box-and-whisker plots

4.3: Distribution properties

1. Quartiles

2. Interquartile range (IQR)

3. Variance & standard deviation

4. Addition, subtraction, and multiplication of constants

5. Outliers

4.4: Introduction to linear statistics

1. Scatter diagrams & correlation

2. Pearson's correlation coefficient

3. Regression lines & prediction

4. Spearman's rank correlation coefficient

5. Pearson's vs Spearman's

4.5: Probability

1. Probability

2. Relative frequency, complements & expected number E(X)

3. Probability diagrams

4. Conditional probability

4.6: Probability distributions

1. Discrete random variables

2. Expected value E(X)

3. Binomial distribution

4. Normal distribution & standardization

4.7: Hypotheses & tests

1. Hypothesis testing

2. Chi-squared test of goodness of fit

3. Chi-squared test for independence

4. The t-test

5. Choosing the correct test

4.8: Data collection & categorisation (HL)

1. Data collection methods

2. Question types & Relevant data

3. Categorising data for chi-squared tests

4. Reliability & validity

4.9: Advanced linear statistics (HL)

1. Non-linear regression

2. Residuals & least squares regression

3. Coefficient of determination

4.10: Linear transformations & combinations (HL)

1. Linear transformations

2. Linear combinations

3. Unbiased estimates

4. The central limit theorem

4.11: Confidence intervals (HL)

1. Confidence intervals

2. Known population standard deviation

3. Unknown population standard deviation

4. Effect of sample size & confidence level

4.12: Poisson distribution (HL)

1. Poisson distribution

2. Finding Poisson probabilities

3. Independent Poisson variables

4. Choosing between distributions

4.13: Distribution tests (HL)

1. Critical values

2. Tests for population means & correlation

3. Binomial test

4. Poisson tests

5. Type I & Type II errors

4.14: Transition matrices (HL)

1. Markov chains & transition matrices

2. State probability matrices

3. Regular Markov chains

4. Long-term behaviour

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Populations & samples

Statistics is about collecting, organising, analysing and interpreting data. In this section, the focus is on types of data, populations and samples, sampling methods, reliability and bias, outliers, frequency distributions, and basic measures of central tendency and spread.

A population is the full group we want to study.
A sample is a smaller group chosen from that population.
A random sample is a sample chosen so that each member of the population has an equal chance of being selected.

If a school wants to study students' study habits, the population might be all students in the school, while a sample might be $50$ students selected from that population.

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