AC9M9ST03Year 9StatisticsPractised on site

AC9M9ST03 — Year 9 Statistics

Official Curriculum Content Description:

represent the distribution of multiple data sets for numerical variables using comparative representations; compare data distributions with consideration of centre, spread and shape, and the effect of outliers on these measures

Worked Examples (2)

Example 1Quartiles & Interquartile Range
For the dataset 15,17,19,23,25,29,3315, 17, 19, 23, 25, 29, 33, calculate the interquartile range (IQR).
Common mistake: Using full Range (max - min) instead of IQR (Anti-pattern: range is distorted by outliers).
Correct Answer:1212
Worked Solution:
1. Lower quartile Q1=17Q_1 = 17. 2. Upper quartile Q3=29Q_3 = 29. 3. IQR=Q3−Q1=29−17=12\text{IQR} = Q_3 - Q_1 = 29 - 17 = 12. Note: IQR ignores outliers, measuring the spread of the middle 50%.
Example 2Five-Number Summary & Box Plots
Two distributions are summarised by their five-number summaries. Distribution A: Min = 55, Q1 = 1010, Median = 1616, Q3 = 2323, Max = 3333. Distribution B: Min = 1010, Q1 = 1818, Median = 2727, Q3 = 3838, Max = 5353. By how much does the greater median exceed the lesser (state the positive difference)?
Common mistake: Comparing the interquartile ranges instead of the medians when comparing two distributions.
Correct Answer:1111
Worked Solution:
1. Median of A =16= 16; median of B =27= 27. 2. ∣MedianB−MedianA∣=11|\text{Median}_B - \text{Median}_A| = 11.

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