Presenting and interpreting the data
What the standard asks for
- Present the data using a range of appropriate methods — the standard defines these as graphs, tables or reports relevant to the research.
- "A range" means more than one form, and "appropriate" means the form suits the data. Six pie charts is not a range.
Choosing the right presentation
| Data | Best shown as | Why |
|---|---|---|
| Parts of one whole (which option was preferred) | Pie chart | Shows shares of 100% at a glance |
| Comparing separate categories (spend by year level) | Bar or column chart | Heights are easy to compare directly |
| Change over time (weekly sales) | Line graph | Shows a trend, not just points |
| Exact figures, or several variables at once | Table | Precise, and lets the reader find any value |
| Reasons and opinions | Selected quotes, grouped by theme | Words cannot be averaged |
Rules that decide whether a graph works
- Every graph needs a title that says what it shows, including the sample size — "Preferred lunch option, n = 80".
- Label both axes, with units.
- Start a bar chart's axis at zero. Starting at 40 makes a small difference look enormous, which misleads.
- Use percentages when comparing groups of different sizes, and give the raw numbers too — "62% (n = 34)".
- One idea per graph. If a chart needs a paragraph to explain, it is doing two jobs.
- Do not graph a question with three responses. Present small numbers as text or a table.
Interpreting — the step most people skip
- Presenting is showing the data. Interpreting is saying what it means.
- Every graph in your report should be followed by a sentence that reads it: "62 of 80 students (78%) said they would buy at $4. The largest group of those who said no gave price as the reason, not the food."
- Then look for what is not obvious:
- Patterns — does the answer differ by year level, by gender, by whether they currently buy lunch?
- Contradictions — do the interviews disagree with the questionnaire? That is a finding, not a problem to hide.
- Outliers — one respondent spending $25 a week will drag an average upwards; report the median as well when one value distorts the mean.
- The size of the group that matters — 78% "yes" among a sample where 60% already buy lunch is a weaker result than it looks.
Reading averages carefully
- The mean is the total divided by the number of values. It is distorted by extreme values.
- The median is the middle value when they are ordered. It is not distorted by extremes.
- Where a few large values exist — spending, for instance — quote both, and say which you are relying on and why.
Worked ExampleReading a result properly
An invented school project surveyed 80 students about a proposed $4 hot lunch. Illustrative results:
| Response | Number | Percentage |
|---|---|---|
| Would buy most days | 18 | 22.5% |
| Would buy sometimes | 44 | 55% |
| Would not buy | 18 | 22.5% |
Of the 80 respondents, 48 said they currently buy something from the canteen; 32 bring lunch from home.
Interpret this result for the business decision.
Step 1 — State the headline
62 of 80 students (77.5%) would buy at least sometimes. On its face, strong support.
Step 2 — Break it down by the group that matters
"Sometimes" is not a purchase. The reliable demand is the 22.5% who would buy most days — 18 students.
If the school has 900 students and this sample is representative, most days demand is roughly 900 × 0.225 ≈ 200 lunches, while "sometimes" is an unknown fraction of the remaining 495 students who chose it.
Step 3 — Check the sample against the population
60% of the sample (48 of 80) already buy from the canteen. If the school as a whole is less than 60% canteen buyers, the sample over-represents existing customers, and existing customers are more likely to say yes.
That means 77.5% is an upper estimate, not a central one.
Step 4 — State the interpretation, with its limits
Around 200 students a day is the planning figure, and it should be treated as an upper estimate because the sample over-represents students who already buy lunch.
The business decision follows: start with a production run well below 200, measure actual sales for two weeks, and scale up on observed demand rather than on stated intention.