Collection and Presentation of Data
What the exam tests
This domain covers how data are gathered and turned into tables, diagrams and graphs. Questions often ask you to classify a source, build a frequency distribution with correct class boundaries, or read a histogram or ogive.
Collection
- Primary data are collected first-hand by the investigator; secondary data are already collected and reused.
- A census covers every unit; a sample survey covers part of the population.
- Common primary methods: direct personal interview, telephone interview, mailed questionnaire, and investigator-filled schedule.
- Check secondary data for reliability, suitability and adequacy before use.
Presentation
A variable is discrete if it takes isolated values and continuous if it can take any value in an interval. In an exclusive class such as 10–20, the upper limit is excluded; in an inclusive class such as 10–19, there is a gap. Convert inclusive to exclusive using correction factor = gap/2, so 10–19, 20–29 becomes 9.5–19.5, 19.5–29.5. Class mark = (lower limit + upper limit)/2; class width = upper boundary − lower boundary.
A histogram has touching bars whose areas are proportional to frequency; with unequal widths use frequency density = frequency/width. A frequency polygon joins class marks. An ogive plots cumulative frequency against class boundaries; the two ogives meet at the median.
Worked example
Classes 10–19, 20–29, 30–39 with frequencies 4, 7, 9. Gap = 1, correction = 0.5. Boundaries: 9.5–19.5, 19.5–29.5, 29.5–39.5. Width = 10. Class marks: 14.5, 24.5, 34.5. Total frequency 20; the less-than ogive plots (19.5, 4), (29.5, 11), (39.5, 20).
Traps
Using stated limits instead of boundaries in a histogram or ogive; forgetting the 0.5 correction; mixing frequency with cumulative frequency; drawing gaps between bars for continuous data.