Data Collection Cheat Sheet - Edexcel Maths A-level

Key Concepts

• Population: The entire set of items of interest in statistics. Data obtained is raw data.
• Census: Measures every member of a population, providing complete accuracy but is time-consuming, expensive, and impractical for large data sets.
• Sample: A subset of the population used to infer information about the population.

Advantages and Disadvantages

• Census:
  • Advantages: Complete accuracy.
  • Disadvantages: Time-consuming, expensive, destructive testing not viable, difficult to process large data.
• Sample:
  • Advantages: Less time, cheaper, fewer responses needed, less data to process.
  • Disadvantages: May lack accuracy, not representative of small subgroups.

Sampling Units

• Sampling Units: Individual units in a population.
• Sampling Frame: A list formed by naming and numbering sampling units.

Random Sampling

• Concept: Every population member has equal selection chance to avoid bias.
• Types:
  • Simple Random Sampling:
    • Each sample has an equal chance.
    • Example: Select 12 members from a yacht club using a random number generator or lottery sampling.
    • Pros: Free of bias, easy and cheap.
    • Cons: Not suitable for large samples, requires sampling frame.

Non-random Sampling

• Quota Sampling:

  • Sample reflects population characteristics.
  • Pros: Representative, no sampling frame, quick, easy, inexpensive.
  • Cons: Can introduce bias, population division costly or inaccurate, non-responses not recorded.

• Opportunity/Convenience Sampling:

  • Sample from available, suitable people.
  • Pros: Easy, inexpensive.
  • Cons: Unlikely to be representative, researcher-dependent.

Data Types

• Quantitative Data: Numerical observations.
• Qualitative Data: Non-numerical observations.
• Continuous Variable: Any value within a range.
• Discrete Variable: Specific set values.

Grouped Frequency Table

• Class Boundaries: Max/min values in a class.
• Midpoint: Average of class boundaries.
• Class Width: Difference between boundaries.

Large Data Set Considerations

• Exams may provide relevant extracts for calculations.

Systematic Sampling

• Process: Select at regular intervals from an ordered list.
• Example: Every 5th person from a population of 100.
• Pros: Simple, quick, suited for large samples.
• Cons: Needs sampling frame, bias if non-random frame.

Stratified Sampling

• Process: Divide population into strata, sample from each.
• Calculation:
  • Number sampled in stratum = (number in stratum / number in population) x overall sample size
• Example: Sample workers from different age groups.
• Pros: Accurate reflection of population structure, proportional representation.
• Cons: Requires clear classification into strata, shares simple random sampling disadvantages within strata.