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
                     (counted)         (measured)

• Discrete — only certain values: number of children, goals scored, shoe size (even where half sizes exist, the set of possible values is still finite and listable).
• Continuous — any value in a range: height, mass, time (limited only by the precision of the measuring instrument used).

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

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

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
Cluster	Whole groups chosen at random	Less precise if clusters differ
Opportunity	Whoever is available	Unrepresentative

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.