Statistical Analysis — Worked Solutions (Preliminary Maths Standard)
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Worked examples for Preliminary Maths Standard statistical analysis. Each shows where the marks are awarded, the key idea, and the full solution explained by your choice of tutor — Stella, Ella or Cassie.
In short: full step-by-step worked solutions for Preliminary Maths Standard — Statistical Analysis. Every question is worked through with the method and reasoning shown, so you can check how to get the answer, not just the final result.
How to use these
Try each question first, then check your working. Use the tutor tabs to read the full solution in the style that suits you: Stella is direct and challenging, Ella is warm and explains the why, and Cassie is concise and analytical.
Example 1 — Classifying data
Question
For each variable below, classify it as categorical or numerical, and then more specifically as nominal, ordinal, discrete or continuous: (a) the brand of a student's phone, and (b) the number of text messages a student sent yesterday.
Solution
Ask two questions for each: is it a category or a number, and then which sub-type.
(a) Brand of phone is a label, not a number, so it's categorical. The brands have no natural order, so it's nominal.
(b) Number of messages is a count, so it's numerical. You can only send a whole number of messages — you count them, not measure them — so it's discrete.
Don't stop at "categorical" or "numerical" — the marks are in the precise sub-type.
Classifying data is a two-step decision, so let's walk through both variables the same way.
First ask: is the data a number or a label? (a) A phone brand like Apple or Samsung is a label, so it's categorical. (b) A number of messages is a count, so it's numerical.
Now the second step — the sub-type. For (a), the brands don't fall into any natural ranking (Apple isn't "more" than Samsung), so it's nominal rather than ordinal. For (b), we ask whether the values are counted or measured: messages come in whole numbers you count, so it's discrete rather than continuous.
Thinking "counted vs measured" is the quickest way to separate discrete from continuous — counting gives whole numbers, measuring gives values along a scale.
Two-step classify for each.
- (a) Phone brand → label → categorical; no order → nominal
- (b) Number of messages → count → numerical; whole numbers → discrete
Where the marks go
- 1 mark: (a) Correctly classified as categorical, nominal
- 1 mark: (b) Correctly classified as numerical, discrete
Key idea
Classify in two steps: categorical (label) vs numerical (number), then the sub-type — nominal/ordinal for categorical, discrete (counted) / continuous (measured) for numerical.
Example 2 — Summary statistics
Question
A student records the number of goals scored in $7$ netball games: $4, 7, 5, 9, 7, 6, 11$. Find the median, the mode, and the range of this data set.
Solution
Order the data first: $4, 5, 6, 7, 7, 9, 11$.
Median is the middle value of $7$ scores — that's the $4$th: $7$.
Mode is the most frequent value. Only $7$ appears twice, so the mode is $7$.
Range is largest minus smallest: $11 - 4 = $ $7$.
Always sort before reading off the median — an unordered list gives the wrong middle.
Before we find any of these, we sort the data into order, because the median depends on position: $4, 5, 6, 7, 7, 9, 11$.
The median is the middle value. With $7$ numbers, the middle one is the $4$th value (three below it, three above), which is $7$.
The mode is the value that appears most often. Scanning the list, $7$ is the only number that repeats, so the mode is $7$.
The range measures the spread — the gap between the highest and lowest: $11 - 4 = 7$.
Sorting first is the habit that protects the median and makes the range easy to read straight off the ends of the ordered list.
Sort: $4, 5, 6, 7, 7, 9, 11$.
- Median: middle of $7$ values = $4$th = $7$
- Mode: only repeated value = $7$
- Range: $11 - 4 = 7$
Where the marks go
- 1 mark: Orders the data set correctly
- 1 mark: Correct median ($7$)
- 1 mark: Correct mode ($7$)
- 1 mark: Correct range ($11 - 4 = 7$)
Key idea
Order the data first, then read off the median (middle value), mode (most frequent value) and range (largest minus smallest).
Frequently asked questions
Step-by-step solutions to Statistical Analysis questions in Preliminary Maths Standard, with the full method shown for each — so you can follow the reasoning, not just the final answer.
Attempt each question yourself first, then compare your method — not just your answer — against the worked solution. The aim is to learn the approach so you can handle unfamiliar questions, rather than memorising answers.
Yes — they follow the NESA syllabus for Preliminary Maths Standard, using the methods and notation expected in exams and assessments.