Data and Its Collection: Revision Notes

Condensed for the final weeks. For the full explanation, use the Data and Its Collection study guide.

Classifying data

                    DATA
          /                      \
   QUALITATIVE                QUANTITATIVE
   (categories)              /            \
                       DISCRETE        CONTINUOUS
                (separate values)   (any value in a range)

• Discrete — takes only certain, separate values: number of children, goals scored, shoe size (even where half sizes exist, the set of possible values is still finite and listable). Discrete data is usually counted, but “counted vs measured” is a usual rule of thumb, not the deciding test.
• Continuous — takes any value in a range: height, mass, time (limited only by the precision of the measuring instrument used). Continuous data is usually measured, but again that is a heuristic, not the definition.

Primary = collected first-hand for this purpose, giving control over exactly what is measured and how. Secondary = already exists, collected by someone else for a different original purpose — faster and cheaper to obtain, but with no control over its accuracy or the exact definitions used.

Class boundaries for continuous data (previewing Topic 3 – Frequency Distributions)

Class boundaries are examined fully under Topic 3, but the underlying idea is needed as soon as continuous data is recorded to a stated accuracy, so it is previewed here. A value recorded to a stated accuracy lies in an interval:

12.4 s to 1 d.p.   ->   12.35 <= t < 12.45
6.3 cm to 1 d.p.   ->    6.25 <= l <  6.35

Lower bound uses ≤, upper bound uses < — the convention avoids two adjacent classes ever overlapping at a shared boundary value.

Census vs sample

	Census	Sample
Coverage	Every member	Part of the population
Accuracy	Complete	Subject to sampling error
Cost/time	High	Lower
Use when	Population small, accuracy vital	Population large, or testing destroys the item

Sampling methods

0479 names four sampling methods (a sampling frame is needed for all of them except quota):

Method	How	Weakness
Simple random	Random numbers; all equally likely	Needs a complete sampling frame
Systematic	Every nth from a random start	Bias if the list is periodic
Stratified	Proportional numbers from each group	Strata must be identifiable
Quota	Set numbers per category, interviewer chooses	Not random; interviewer bias

Background – not among the methods 0479 names. Cluster sampling (whole groups chosen at random; less precise if clusters differ) and opportunity sampling (whoever is available; unrepresentative) are common wider sampling vocabulary. The syllabus does not name either, so learn the four above first and treat these two as background. (The syllabus’s own example of a biased method – surveying the first people to arrive – is in effect an opportunity sample.)

Stratified sample size = (group size ÷ population) × sample size. Round so the parts still total correctly.

Worked example. A school of 900 students has 400 in Key Stage 3, 350 in Key Stage 4 and 150 in Key Stage 5. Take a stratified sample of 60.

Sampling fraction = 60 / 900 = 1/15

KS3: 400 / 15 = 26.7  -> 27
KS4: 350 / 15 = 23.3  -> 23
KS5: 150 / 15 = 10    -> 10
                        ---
                        60

Round carefully so the parts still total the sample size — a frequent source of a lost mark when two roundings go the same way.

Questionnaire design

A good questionnaire uses clear, unambiguous language, avoids leading questions, provides response options that do not overlap and cover every possibility, and keeps sensitive questions to the end. A pilot survey tests it on a small group first, exposing ambiguous wording before the full survey runs.

Bias

Sources: incomplete sampling frame, non-response, self-selection, leading questions, interviewer effect — and, for a questionnaire specifically, overlapping or non-exhaustive response options.

A larger sample reduces sampling error but does NOT remove bias. A biased method stays biased at any size — the two concepts (random sampling error, and systematic bias in the method) are frequently confused but need to be argued separately.

Exam traps

• Shoe size is discrete, even with half sizes — the deciding factor is a finite, listable set of possible values, not whether the values look like “whole numbers”.
• Never write overlapping classes (10–20, 20–30).
• Stratified means proportional, not equal, numbers from each group.
• Systematic sampling still needs a random start.
• Upper bound uses < , not ≤ .
• Writing a leading or ambiguous question, or overlapping response options, in a questionnaire design question.
• Rounding all three parts of a stratified sample up (or all down) without checking the total still matches the required sample size.

Self-test

1. Classify: eye colour, number of siblings, mass of a parcel.
2. A school has 300 girls and 200 boys. Take a stratified sample of 50.
3. State the class boundaries of a time recorded as 9.7 s to 1 d.p.
4. Give two sources of bias in a survey.
5. Why does increasing sample size not remove bias?
6. What is the purpose of a pilot survey?
7. A population of 900 splits into groups of 400, 350 and 150. Find the stratified sample sizes for a total sample of 60.

Answers: 1. Eye colour = qualitative; number of siblings = discrete quantitative; mass = continuous quantitative. 2. Fraction 50/500 = 1/10 → 30 girls and 20 boys. 3. 9.65 ≤ t < 9.75. 4. Any two: incomplete sampling frame, non-response, self-selection, leading questions, interviewer effect. 5. Bias is a systematic error in the method — it shifts every result in the same direction, so collecting more data under the same flawed method simply produces more biased data. 6. To test the questionnaire on a small group first, exposing ambiguous or unclear wording before the full survey is run. 7. 27, 23 and 10 (sampling fraction 1/15, rounded so the parts total 60).

For the full worked explanation with additional detail, see the Data and Its Collection study guide; for exam-style questions with full mark schemes, see the Data and Its Collection practice questions.