Free IB Maths AA SL lesson: Variance and standard deviation of X (extension)
A ready-to-teach IB Maths AA SL lesson on Variance and standard deviation of X (extension) (Unit 4 · Statistics & Probability): editable slides and teacher notes, free; a printable worksheet in 3 levels with answers for school plans. About 55 minutes.
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What's inside
- Slides (PowerPoint, editable) · freeabout 12 slides: do now, objectives, key ideas, a worked example step by step, “your turn”, practice QR code, exit ticket
- Teacher notes (PDF) · freelesson plan with timings, common mistakes, homework links
- Worksheet (PDF) · school plans6 questions, 37 marks: Fluency, Reasoning, Exam-style. Included with school plans and the teacher trial.
- Answers (PDF) · school plansthe answer to every worksheet question, from its mark scheme. Included with school plans and the teacher trial.
Learning objectives
- Variance and standard deviation
Key ideas on the slides
- Variance σ² = (Σ (x − x̄)²)/n = (Σ x²)/n − x̄²; standard deviation σ = √variance.
- From a frequency table: σ² = (Σ fx²)/(Σ f) − x̄².
- The standard deviation measures the typical distance of values from the mean, in the same units as the data.
- IB uses the population standard deviation (σₓ on the GDC); A Level uses (Sₓₓ)/n with Sₓₓ = Σ x² − ((Σ x)²)/n (or n − 1 where stated).
By the end of the lesson, students should be able to answer a question like: Find Var(X) for a distribution where E(X)=2 and E(X^2)=5.4.
Key vocabulary
- variance: The mean of the squared deviations from the mean.
- standard deviation: The square root of the variance.
- deviation: x − x̄, how far a value is from the mean.
Common mistakes this lesson tackles
- Subtracting x̄ instead of x̄² in (Σ x²)/n − x̄².
- Forgetting to square-root the variance.
- Using s (n − 1) when the course asks for σ (or the reverse).
Calculator tips
- 1-Var Stats: read σₓ (population) or sₓ as your course requires.
Where this lesson fits
Variance and standard deviation of X (extension) is in Unit 4 · Statistics & Probability of the IB Maths AA SL scheme of work.
- The lesson before: Binomial distribution (scheme-of-work lessons: Comparing Distributions; Cumulative Probabilities in Context)
- The next lesson: Normal distribution (probability lookups) (scheme-of-work lessons: The Standard Normal Curve; Distributions in Context: Normal Probabilities Feeding a Binomial Model; Standardisation & z-values)
Lesson plan
| 0–5 min | Do now: students write down what they remember about Binomial distribution and Discrete random variables & E(X) |
| 5–8 min | Share the learning objective and success criteria |
| 8–20 min | Teach: the worked example, step by step; students copy the method |
| 20–25 min | Your turn: 1 mini-whiteboard question; check every board before moving on |
| 25–42 min | Practise: the worksheet (6 questions in 3 levels, with school plans and the teacher trial) or the topic's practice questions online; move up a level after two right in a row |
| 42–47 min | Plenary: 1-question exit ticket; collect it to plan the next lesson |
For students: practise this topic
The worksheet's QR code opens the IB Maths AA SL Unit 4: Discrete Random Variables practice questions.
With a school plan
Set Variance and standard deviation of X (extension) as homework marked by AI, print this lesson's levelled worksheet with answers, and rebuild the lesson for your class with Create lesson. Free for 30 days as a teacher, no card.
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