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📖 Lesson 20 ⏱ ~30 min Year 10 · Unit 4 ⚡ +50 XP

Statistics and Probability Review

Consolidate all statistics and probability concepts through mixed exam-style problems and revision.

Today's hook:
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Core learning
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Worksheet

Worksheet

Use the worksheet to complete this lesson in your book or digitally.

Warm-up
Think First
+5 XP each

Q1 · Looking back at this unit, what is one thing about statistics or probability that surprised you or changed how you think?

Q2 · How might you honestly use statistics and probability in a future career or an everyday decision you will face?

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Intentions

Learning Intentions

Know

  • All statistical displays, measures of centre and spread, bivariate analysis, and probability techniques covered in this unit.

Understand

  • How to select the appropriate statistical or probability technique for a given problem or data set.

Can Do

  • Solve mixed problems confidently and justify choices of display, measure and technique.
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Key Terms

Key Terms

Statistical investigation — The process of formulating questions, collecting data, analysing and drawing conclusions.
Justification — Providing reasons for choosing a particular method or reaching a conclusion.
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Misconceptions

Misconceptions to Fix

✗

Wrong: Theoretical probability is always more accurate than experimental probability.

✓

Right: Theoretical probability assumes a fair/random experiment. Experimental probability may be more accurate if the theoretical assumptions are wrong (e.g., a biased coin).

✗

Wrong: The Law of Large Numbers means that after many trials, the experimental probability will exactly equal the theoretical probability.

✓

Right: The Law of Large Numbers says experimental probability approaches theoretical probability as the number of trials increases. It does not guarantee exact equality.

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Content

Statistics and Probability Review

Work through the content, activities and worked examples below. Test your understanding with the questions in the Questions phase.

Remember Review checklist: Can you classify data? Calculate mean, median, mode, range, IQR? Draw and interpret box plots, histograms, scatter plots? Calculate basic and conditional probability?
HSC Note In the exam, always show your working clearly. For probability questions, write fractions before converting to decimals. For statistics questions, state the formula you are using.
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From the lesson
Activity
✏ Activity 1 — Mixed Revision

Complete the following mixed problems:

  1. A data set has values: 12, 15, 18, 21, 24, 27, 30. Find the mean, median, range and IQR.
  2. A bag contains 3 red, 4 blue and 5 green marbles. Two marbles are drawn without replacement. Find P(both blue).
  3. A scatter plot shows a strong negative correlation between temperature and heating costs. Interpret this result.
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From the lesson
Worked Example

Worked Example

Step-by-step
A survey of 50 students found that 30 own a mobile phone, 25 own a laptop, and 15 own both. Find the probability that a randomly chosen student owns a mobile phone given they own a laptop.
  1. 1
    Step 1: Given that the student owns a laptop, restrict to the 25 laptop owners.
  2. 2
    Step 2: Of these 25, 15 also own a mobile phone.
  3. 3
    Step 3: P(mobile | laptop) = 15/25 = 3/5 = 0.6.
  4. 4
    Step 4: Using the formula: P(mobile and laptop) = 15/50 = 0.3, P(laptop) = 25/50 = 0.5. P(mobile | laptop) = 0.3/0.5 = 0.6. ✓
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From the lesson
Revisit

Revisit Your Thinking

Look back at your Think First response. What new understanding do you have now?

Reflect
Revisit your thinking
reflect

Earlier you were asked: What was your first thought on this topic?

Now that you've worked through the lesson, write a fuller answer. What changed in your thinking?

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Multiple Choice

Multiple Choice

Select the best answer for each question.

1 mark The most appropriate display for comparing the heights of two groups is:

1 mark To show the relationship between hours studied and exam score, use:

1 mark If a data set has an outlier, the best measure of centre is:

1 mark Drawing two cards without replacement from a deck creates:

1 mark P(A|B) = P(A) when:

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Short Answer

Short Answer

Show all working and justify your answers.

1. 4 marks The test scores of 10 students are: 45, 52, 58, 62, 65, 68, 72, 75, 80, 95.
(a) Calculate the mean and median.
(b) Calculate the range and interquartile range.
(c) Which measure of centre best represents this data set? Justify your answer.

2. 4 marks A coin is biased so that P(head) = 0.6. The coin is flipped 3 times.
(a) Draw a tree diagram.
(b) Find P(exactly 2 heads).
(c) Find P(at least 1 head).

3. 3 marks A scatter plot shows the relationship between study time and test score. Describe how you would determine whether the correlation is positive, negative or none, and explain how you would draw a line of best fit.

Marking guidance: 1 mark each for MCQs. See mark allocations for each short answer question.

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