AscentIQAscentIQ — home
← IB Math AA SL

IB Math AA SL · Topic 4

Statistics and probability

Data, then chance, then the two distributions that connect them. The first half describes what has been observed — samples, spread, correlation — and the second models what could be: probability, the binomial and the normal. The calculator does the arithmetic. The marks are for stating what you asked it.

What the syllabus covers

Twelve assessed sections, SL 4.1 to 4.12 — the most sections of any topic, ending with conditional probability and standardisation.

SL 4.1Collecting data and samplingPopulation and sample, random and other sampling methods, bias, reliability of sources, and the interpretation of outliers.
SL 4.2Presenting dataFrequency tables, histograms, cumulative frequency graphs and box-and-whisker diagrams.
SL 4.3Central tendency and dispersionMean, median, mode and modal class; the interquartile range, standard deviation and variance; the effect of a constant change on the data.
SL 4.4Linear correlation and the regression line of y on xScatter diagrams, Pearson's r, the regression line used for prediction, and the meaning of its gradient and intercept.
SL 4.5Concepts of probabilityTrials, outcomes, sample space and events; complementary events; the expected number of occurrences.
SL 4.6Combined, conditional and independent eventsVenn diagrams, tree diagrams, sample-space diagrams and tables; mutually exclusive events and the addition rule.
SL 4.7Discrete random variablesProbability distributions as tables and expected value, with applications.
SL 4.8The binomial distributionWhen it applies, probabilities with technology, and its mean and variance.
SL 4.9The normal distributionIts properties and diagram; normal probabilities and inverse normal calculations with technology.
SL 4.10The regression line of x on yThe second regression line, and when it — rather than y on x — is the one to predict with.
SL 4.11Conditional probability and independenceThe formal definition P(A | B) = P(A ∩ B) / P(B), and the test for independence.
SL 4.12Standardisation of normal variablesz-values, and inverse normal calculations where the mean, the standard deviation or both are unknown.

How it is examined

Technology is expected for the distributions and for the regression. The no-calculator paper tests the same ideas with clean numbers.

  • On Paper 2 the GDC produces standard deviation, r, the regression line, binomial and normal probabilities. It is not the answer on its own: the guide expects the working to say what was entered — the distribution, its parameters, the interval.

  • On Paper 1 the same topics appear without a calculator: probabilities read from a table, Venn or tree diagram as exact fractions, a z-value you can find by hand, a mean from a frequency table, the effect of a transformation on the mean and the standard deviation.

  • Write the model before you use it: X ~ B(n, p) or X ~ N(μ, σ²), with the numbers. That line is where the method mark lives, and it is also what stops you using the wrong distribution.

  • For discrete variables the inequality matters: P(X < 5) is P(X ≤ 4). The calculator's cumulative function counts 'at most', so converting 'fewer than' and 'more than' is part of the setup.

  • Regression gives two lines. Predicting y from x uses the line of y on x; predicting x from y uses the line of x on y. Predicting outside the range of the data is an extrapolation, and a comment on its reliability is often asked for.

  • The test for independence (SL 4.11) compares numbers: P(A ∩ B) with P(A)P(B), or P(A | B) with P(A). The conclusion is a sentence that names the comparison, not the word 'independent' on its own.

  • Standardisation (SL 4.12) with an unknown mean or standard deviation sets up one or two equations in z-values, and then solves them — a few lines of algebra after one inverse-normal call.

A marked question, mark by mark

A conditional-probability question where the numbers are right and the conclusion is not supported — the usual place a reasoning mark disappears.

Rehearse the setup, not just the arithmetic

From SL 4.1 sampling to SL 4.12 standardisation, every generated exercise comes back with each mark awarded or withheld and a reason — including the model statements and conclusions students habitually leave out.

Start your trial

New to the codes? M1, A1, R1 explained →

Independence · SL 4.11

Seed 8D33

For events A and B, P(A) = 0.4, P(B) = 0.5 and P(A ∩ B) = 0.2.

  1. (a)Find P(A | B).
  2. (b)Determine whether A and B are independent, justifying your answer.

Your work

P(A | B) = P(A ∩ B) / P(B) = 0.2 / 0.5 = 0.4

A and B are independent.

Marks awarded

  • M1Mark awarded. Correct definition of conditional probability with the values substituted.
  • A1Mark awarded. P(A | B) = 0.4.
  • R1Mark not awarded. 'Independent' is stated, but no comparison is made: P(A | B) = 0.4 equals P(A) = 0.4 is the justification, and it is missing.

Where marks are actually lost

Here the calculator is rarely the problem. The setup around it, and the sentence after it, are.

Computing P(X < 5) as P(X ≤ 5) because the calculator only offers 'at most'.

CostThe probability is for the wrong event, so the accuracy mark is lost even though the distribution and the parameters were correct.

Quoting a calculator result without writing the distribution and its parameters.

CostThe method mark is for the model you chose; a bare number from a screen leaves nothing to award it to.

Predicting x from the line of y on x, or the reverse.

CostThe regression lines are different lines. Using the wrong one gives a wrong prediction and a lost accuracy mark.

Concluding 'independent' or 'not independent' without writing the comparison that decides it.

CostThe reasoning mark is for the comparison and what it shows. The word on its own earns nothing.

Other Math AA SL topics

Studying a different course?