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Year 9–10 · Year 9–10 Maths

Year 9–10 Maths — Statistics and Probability

Updated 16 July 2026

Year 9–10 statistics extends beyond basic measures of centre to box plots, bivariate data and more complex probability. The concepts of quartiles, correlation and independent/dependent events all appear in VCE Methods and in real-world data analysis.

Key Concepts & Formulas

  • Five-number summary: minimum, lower quartile (Q1), median (Q2), upper quartile (Q3), maximum

  • IQR (interquartile range) = Q3 − Q1; measures spread of the middle 50% of data

  • Box plot (box-and-whisker): displays five-number summary; whiskers extend to min and max (or to 1.5 × IQR)

  • Outlier: a data point more than 1.5 × IQR below Q1 or above Q3

  • Scatter plot: displays two numerical variables; used to identify correlation

  • Correlation: positive (both increase together), negative (one increases as other decreases), no correlation

  • Correlation does not imply causation — two variables can be correlated without one causing the other

  • Tree diagram: shows all possible outcomes for multi-step probability experiments

  • Multiplication rule: P(A and B) = P(A) × P(B) for independent events; P(A) × P(B|A) for dependent events

  • Two-way table: organises data by two categorical variables; read probabilities directly from the table

Practice Questions

4 questions

Attempt each question before reading the hint. These are styled to match school assessment format.

Q1.A dataset: 3, 7, 8, 10, 12, 15, 18, 21, 25. Find Q1, Q2 and Q3, and draw a box plot.

4 marks

Q2.A bag has 4 red and 6 blue marbles. Two marbles are drawn without replacement. Find the probability both are red.

3 marks

Q3.A scatter plot shows a negative correlation between hours of TV watched per day and exam scores. Describe what this means and explain why it does not prove TV causes lower scores.

3 marks

Q4.200 students are surveyed: 80 play sport, 60 play music, and 30 do both. Fill in a two-way table and find the probability that a randomly chosen student plays neither sport nor music.

4 marks

Common Mistakes to Avoid

These are the errors that students most frequently make in Statistics and Probability — and that examiners are specifically watching for.

  • Confusing IQR (Q3 − Q1) with range (max − min) — they measure different aspects of spread

  • In probability trees, not multiplying along branches to find compound probabilities

  • Stating that correlation proves causation — always note that correlation only shows an association

  • Forgetting to adjust probabilities in "without replacement" problems — the denominator changes each time

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