IB Maths AA 4.3 Notes

This page contains our IB Maths AA notes for 4.3. By reading each one of these notes, you will fully cover the content for IB Maths AA 'Distribution properties'.

All Topic 4 Sub-topics 4.1: Fundamentals Of Statistics 4.2: Visualising Statistics 4.3: Distribution Properties 4.4: Linear Statistics 4.5: Probability 4.6: Probability Distributions (HL)4.7: Bayes theorem (HL)4.8: Advanced distribution properties

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Chapters

1. Quartiles

2. Interquartile range (IQR)

3. Variance & standard deviation

4. Addition, subtraction, and multiplication of constants

5. Outliers

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Quartiles

Quartiles divide an ordered discrete data set into four parts.

$Q_1$ marks the point below which about $25\%$ of the data lies.
$Q_2$ is the median.
$Q_3$ marks the point below which about $75\%$ of the data lies.

Technology is used to find quartiles for discrete data, and different methods may give different answers.

Consider the ordered data set $1,2,3,4,5,6,7,8,9$ . Find the median, $Q_1$ , $Q_3$ , and the $IQR$ .
The median is $5$ .
A calculator may then give quartiles around $Q_1=2.5$ and $Q_3=7.5$ , so $IQR=7.5-2.5=5$ .

A different method might give slightly different quartiles, which is why the use of technology is emphasised.

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