Unit 4
Statistics and Probability
About this unit
Calculate means and averages, interpret column and line graphs, work with Venn diagrams, and apply basic probability reasoning to single and compound events.
What types of questions will you face?
- 1Find the average of one sub-group when you know the overall average and the average of the other sub-group — use the total-sum method (mean × count = total) applied to each part
- 2Evaluate three probability statements about a bag of coloured items — write each probability as a fraction, compare numerators, and apply the complement rule for 'not [colour]' claims
- 3Read a column graph or pictograph to calculate totals, differences between groups, or per-symbol values — then answer a follow-up question about the data
- 4Calculate a weighted mean when groups of different sizes have different averages — find each group total first, then combine before dividing
- 5Determine the mean, median, or mode from a small data set given in a table, then verify which of several claims about the data are correct
Skills you will build
- Converting between mean and total: total = mean × count (and back) — the essential move in every split-group or combined-group averages question
- Writing probabilities as fractions over the total and comparing by inspecting numerators rather than converting to decimals
- Applying the complement rule correctly: P(not A) = 1 − P(A) = sum of all other probabilities — essential for statement 3 in multi-claim questions
- Reading bar charts and pictographs accurately: reading bar heights, computing differences between bars, and finding the value one symbol represents
- Checking each probability or data claim independently before matching to a statement-combination option — never trust intuition on these
By the end of this unit, you will be able to
- Solve any split-group or multi-group averages problem using the total-sum method, without guessing
- Evaluate probability statements systematically and identify the correct combination of true statements
- Extract exact values from column graphs, pictographs, and data tables to answer questions accurately under time pressure
- Combine averages from groups of different sizes into a single weighted mean
- Find the mean, median, and mode of a small data set and assess whether given claims about them are true or false
Difficulty profile
Questions in this unit range from Very Easy to Very Difficult. Simple mean questions and basic graph reading are Very Easy to Easy. Multi-statement probability and split-group averages questions are Medium to Difficult. Weighted means and claim-evaluation questions on graphs can reach Very Difficult.
Exam tip: Statistics and Probability
For any averages question, your very first move is to convert every mean into a total (multiply mean × count). Never reason about averages directly — work with totals, subtract where needed, then divide at the end. For probability statements, write all fractions over the same denominator before comparing — and always check the 'not' statement using the complement: count of non-target items divided by total.
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