Data And Its Collection

O Level Statistics 4040 – Detailed Notes
Chapter 1: Data and Its Collection
Written and Compiled By Sir Hunain Zia, World Record Holder With 154 Total A Grades, 7 Distinctions and 11 World Records For Educate A Change O Level And IGCSE Statistics Full Scale Course

1.1 General Ideas of Sampling

• Population
  • Entire group of individuals or items under study.
  • Example: All students in a school.
• Census
  • Data is collected from every member of the population.
  • Advantages: Accurate, complete.
  • Disadvantages: Time-consuming, expensive, impractical for large populations.
• Sample
  • Subset of the population selected for the study.
  • Advantages: Less time, lower cost, feasible for large populations.
  • Disadvantages: May not represent the whole population well if not selected properly.
• Representative Sample
  • A sample that accurately reflects the characteristics of the population.
  • Minimizes bias and improves reliability of results.

1.2 Types of Sampling

1. Simple Random Sampling

• Every individual has an equal chance of selection.
• Selection is purely by chance.
• Method: Random number tables or generators.
• Advantages: Unbiased, easy to understand.
• Disadvantages: Difficult without full population list, may be impractical.

2. Systematic Sampling

• Selecting every kth individual from a list after a random start.
• If population = 1000 and sample size = 100, then k = 1000/100 = 10.
• Advantages: Simple, evenly spread.
• Disadvantages: May be biased if there’s a hidden pattern in the list.

3. Stratified Sampling

• Population is divided into distinct groups (strata) based on a characteristic (e.g., age, gender).
• Random samples taken from each stratum proportionally.
• Advantages: More representative, accounts for subgroup differences.
• Disadvantages: Requires knowledge of strata and population breakdown.

4. Quota Sampling

• Researcher selects a specific number of subjects from each group.
• Non-random; interviewer chooses participants who meet criteria.
• Advantages: Quick, easy to manage.
• Disadvantages: Subjective, prone to bias.

Use of Random Numbers

• Essential for reducing selection bias in simple random and stratified sampling.
• Random number tables or digital random number generators are used.
• Ensures impartial selection.

1.3 Bias: How It Arises and Is Avoided

Definition

• Bias is a systematic error in the way data is collected, leading to misleading results.

Sources of Bias

• Poor sampling method (e.g., only surveying friends).
• Non-representative samples.
• Leading or loaded questions.
• Non-response from certain groups.
• Interviewer influence.

How to Avoid Bias

• Use random sampling.
• Ensure sample is large and diverse enough to be representative.
• Design neutral and clear questions.
• Provide anonymity to respondents.
• Avoid convenience sampling unless justified.

1.4 General Ideas of Surveys

• Surveys are tools to collect data from a sample or population.
• Used in business, health, politics, education, etc.

Key Components

• Clear objective and target population.
• Well-designed questionnaire (open/closed questions).
• Effective sampling method.
• Proper data recording and analysis.

Question Types

• Closed Questions
  • Provide specific options (e.g., Yes/No, multiple choice).
  • Easy to analyze statistically.
  • May limit depth of response.
• Open Questions
  • Allow detailed, free-form answers.
  • Rich data, but harder to analyze.

Designing a Good Questionnaire

• Use clear, unambiguous language.
• Avoid leading or biased questions.
• Keep it concise and relevant.
• Pre-test with a small group.

1.5 Types of Data and Variable

Data Types

• Qualitative Data
  • Descriptive, non-numerical.
  • Examples: colors, opinions, brands.
• Quantitative Data
  • Numerical, measurable.
  • Examples: height, temperature, marks.

Types of Quantitative Data

• Discrete Data
  • Countable, takes specific values only.
  • Example: number of students in a class.
• Continuous Data
  • Measurable, can take any value within a range.
  • Example: weight, height, time.

Variable

• A characteristic that can vary from one individual or item to another.
• Examples: age, income, test score.

Quick Recap Table

Written and Compiled By Sir Hunain Zia, World Record Holder With 154 Total A Grades, 7 Distinctions and 11 World Records For Educate A Change O Level And IGCSE Statistics Full Scale Course