Lesson 116 — Collecting Data for Discrete and Continuous Variables
Strand: Statistics | Descriptor: AC9M7ST03 | Duration: 45 minutes
Equipment: as required by student plans — rulers, tape measures, timers, scales.
Block note. Stage 2 of the investigation begun in Lesson 115. Students collect their own data this lesson and carry it into Lesson 117 for analysis.
Learning Intentions
- To collect data accurately according to a stated procedure.
- To record and organise raw data ready for analysis.
Success Criteria
I can:
- Follow my collection procedure consistently for every observation.
- Record raw data clearly, with units and the agreed precision.
- Organise raw data into a frequency table.
- Identify and report problems encountered during collection.
Warmup
(6 minutes — protocol check, pairs)
Before collecting anything, answer these about your own plan:
- What exactly are you measuring, in one sentence?
- To what precision?
- Who will you measure, and how many?
- What will you do if a measurement looks wrong?
- Where will the raw data be written down?
The Q4 discussion is the important one. Collect answers. The correct protocol: record it anyway, mark it as questionable, and note why you doubted it. Deciding after the fact which values to keep is how data gets quietly manipulated.
The rule to record: record everything; decide nothing during collection.
Activities
Activity 1 — Explicit Instruction: Collecting Well (10 min)
Four practices that make data trustworthy:
| Practice | Why it matters |
|---|---|
| Consistent procedure | Every observation measured the same way, or the values are not comparable |
| Stated precision | Everyone rounds identically |
| Raw data first | Tallying while measuring loses the original values |
| Note anomalies | An unusual reading with a noted cause is data; an unexplained one is a mystery |
The recording sheet — model this on the board:
| Obs. | Value | Notes |
|---|---|---|
| 1 | ||
| 2 | ||
| 3 | tape slipped, re-measured — this is the second attempt | |
| … |
Two columns are not optional. The Notes column is where honesty lives: re-measurements, interruptions, and doubts all go there, and they become the limitations section of the report (Lesson 118).
Sample size — a brief but real point. More observations give a more reliable picture, but each takes time. For a one-lesson class investigation, aim for at least
I do — demonstrate the ruler-drop test as a worked example of a precise procedure:
- The catcher’s thumb and finger are open
cm apart at the ruler’s mark. - The dropper releases without warning, within
seconds. - Read the centimetre mark at the top of the thumb.
- Record to the nearest
cm. - Discard nothing; note any early grab in the Notes column.
Ask: which of the five steps would people most likely do differently? (Step 3 — where exactly on the thumb — which is why it is specified.)
Activity 2 — Collect the Data (22 min)
Pairs, executing their Lesson 115 plans. The bulk of the lesson.
The requirements:
- Follow the procedure exactly, every time.
- Record raw values with units in a two-column sheet.
- Aim for at least
observations. - Note every anomaly, interruption or doubt.
- When collection is finished, build a frequency table (grouped if continuous).
Circulating prompts:
| Prompt | Purpose |
|---|---|
| Show me your Notes column — what has happened so far? | Makes note-taking a live expectation. |
| Are you rounding the same way every time? | Precision consistency. |
| That value looks odd — what will you do with it? | Rehearses the record-don’t-decide rule. |
| How many observations so far? Will you reach | Sample size management. |
| Has your procedure changed since you started? | A mid-collection change makes the early and late data incomparable — a genuine limitation to note. |
For pairs collecting two samples (comparison studies): keep the two data sets on separate sheets, clearly labelled, with the same procedure and precision for both. A difference in procedure between groups would confound the comparison entirely.
Early finishers: collect more observations, or a second variable for comparison. Do not start analysing — that is next lesson, and rushing it produces displays built on incomplete data.
Activity 3 — Organise and Reflect (7 min)
Individually, then a quick share.
Before you pack up:
- Count your observations. Record the total.
- Complete your frequency table (grouped into intervals if continuous).
- Check: do your frequencies total your number of observations?
- Write two sentences: what went well in collection, and what caused difficulty.
The Q3 check is not optional — a frequency table whose total does not match the raw count contains an error, and finding it now is far cheaper than finding it mid-analysis.
Share round: each pair reports one collection difficulty in a sentence. Collect the common themes on the board — they will reappear as limitations in every report.
Expected themes: inconsistent measuring technique; participants not following instructions; time pressure limiting sample size; self-reported data being unreliable; equipment limitations.
Checks for Understanding
(5 minutes — exit ticket, collected with the data sheet)
- How many observations did you collect?
- State your variable, its units and its precision.
- Give one entry from your Notes column, or state that there were none and why that is plausible.
- Does your frequency table total match your raw count? Show the check.
- Reasoning. Why must an unusual value be recorded rather than discarded during collection?
Answers: 1–4. Student’s own, marked against the data sheet; 5. Deciding which values to keep while collecting lets expectations shape the data. Recording everything and explaining anomalies later keeps the decision visible and reviewable — and the value may be genuine.
Common Misconceptions
| Misconception | How to pre-empt it |
|---|---|
| Discarding odd values on the spot. | The warmup’s Q4 and the record-don’t-decide rule. |
| Tallying instead of recording raw values. | Lesson 107’s protocol, re-enforced in the recording sheet. |
| Changing the procedure partway. | Named as a limitation during circulation. |
| Treating a small sample as sufficient. | The |
| Leaving the Notes column empty by default. | Circulating prompt asks to see it. |
| Starting analysis before collection is complete. | Explicitly deferred to Lesson 117. |
Enrichment — Competition-Style Problems
E1 (Kangaroo style). A student collects
Answer
A value has been tallied twice, or a tally mark added in error. The raw list is the authority — recount against it.
E2 (AMC Junior style). Two students measure the same
Answer
Not safely — combining precisions makes the coarser data misleadingly precise-looking and distorts any grouped display. Either re-measure or round all values to the coarser precision, stating that this was done.
E3 (Challenge). A pair measures reaction times, then realises after
Answer
Either (a) discard the first
E4 (Challenge). Why does increasing a sample from
Answer
Doubling a small sample halves the influence of each individual observation, sharply reducing the effect of chance. Adding
Homework
- Write up your raw data neatly, with units and precision stated at the top.
- Complete your frequency table (grouped if continuous), and show the check that the frequencies total your observation count.
- Write three sentences on your collection: what you did, what went well, and what caused difficulty.
- List every entry from your Notes column, or explain why there were none.
- State your sample size and comment on whether you think it is sufficient, with a reason.
- Name two ways your collection could be improved if you repeated it.
- Predict, from a glance at your raw data, whether the distribution will be symmetric or skewed — and say what makes you think so.
- Reasoning. Explain why raw data must be recorded before tallying.
- Reasoning. Explain why a mid-collection change of procedure is a problem, and what should be done about it.
- Challenge. Suppose your sample were doubled. Predict what would change about your results and what would stay roughly the same, with reasons.
Answers: Q1–7 — student’s own. Q8 — tallying destroys the original values, making it impossible to recheck, to recalculate with different intervals, or to find individual errors. Q9 — early and late observations are then measuring subtly different things, so combining them is invalid; either re-collect under one procedure or analyse the sets separately, and report the change. Q10 — the centre (median/mean) would likely stay similar if the sample is representative; the shape would become clearer and less lumpy; the range would probably widen slightly, since more observations give more chances of an extreme value.