Data And Its Collection
O Level Statistics 4040 – Quiz: 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
Multiple Choice Questions
- Which of the following sampling methods ensures each member of the population has an equal and independent chance of selection?
- A) Quota Sampling
- B) Stratified Sampling
- C) Simple Random Sampling
- D) Systematic Sampling
- Which technique involves dividing the population into groups and randomly sampling from each group proportionally?
- A) Cluster Sampling
- B) Stratified Sampling
- C) Quota Sampling
- D) Simple Random Sampling
- In which sampling method does the researcher select every 10th individual from a list?
- A) Quota
- B) Stratified
- C) Systematic
- D) Random
- A survey question asks: “Don’t you agree that school uniforms are necessary?” What type of bias does this introduce?
- A) Response Bias
- B) Sampling Bias
- C) Non-Response Bias
- D) Leading Question Bias
- Which of the following is not a characteristic of a representative sample?
- A) Proportional to the population
- B) Free from bias
- C) Smallest possible size
- D) Random selection
- A government wants to survey the income of households in different income brackets. Which sampling method is most suitable?
- A) Simple Random Sampling
- B) Cluster Sampling
- C) Stratified Sampling
- D) Convenience Sampling
- Which of the following is an example of qualitative data?
- A) Age in years
- B) Shoe size
- C) Eye color
- D) Number of children
- Discrete data:
- A) Can take any value within a range
- B) Includes measurements like height
- C) Is only categorical
- D) Takes specific, countable values
- What type of data is “temperature in °C”?
- A) Qualitative
- B) Quantitative Discrete
- C) Quantitative Continuous
- D) Categorical
- Which of the following leads to non-response bias?
- A) Survey question is misleading
- B) People selected do not respond
- C) Responses are inaccurate
- D) Sampling frame is incorrect
- Which best describes quota sampling?
- A) Uses random numbers to select
- B) Selects until group quotas are filled
- C) Every kth person is chosen
- D) Divides population into strata and samples from all
- The use of a sampling frame is least necessary in:
- A) Systematic Sampling
- B) Stratified Sampling
- C) Quota Sampling
- D) Simple Random Sampling
- Which is not a valid way to reduce survey bias?
- A) Use of random samples
- B) Leading questions
- C) High response rate
- D) Balanced question wording
- What is the main drawback of a census?
- A) Data is always inaccurate
- B) Only qualitative data is collected
- C) Expensive and time-consuming
- D) Cannot be used for large populations
- Which data set is an example of continuous data?
- A) Number of students
- B) Height in cm
- C) Age in completed years
- D) Shoe size
- The process of selecting units from a population is called:
- A) Data representation
- B) Census
- C) Sampling
- D) Experimentation
- Which method is most likely to produce biased results?
- A) Simple random sampling
- B) Convenience sampling
- C) Systematic sampling
- D) Stratified sampling
- A sample that includes only those who are easily available is called:
- A) Cluster sample
- B) Snowball sample
- C) Convenience sample
- D) Stratified sample
- What is the role of random numbers in sampling?
- A) To ensure stratification
- B) To introduce variation
- C) To reduce bias
- D) To increase convenience
- A population refers to:
- A) The group we draw a sample from
- B) A group of survey respondents
- C) Only a subset of data
- D) The statistical results of an experiment
- Which question is closed?
- A) What do you think of school facilities?
- B) How can the government improve healthcare?
- C) How old are you?
- D) Describe your opinion about your teachers.
- An open question:
- A) Always has yes/no answer
- B) Allows respondents to elaborate
- C) Can be answered by ticking a box
- D) Always yields numerical data
- The key distinction between a sample and a census is:
- A) Accuracy
- B) Time taken
- C) Sample only examines part of population
- D) Census uses qualitative data
- The type of variable where values are obtained by measurement is:
- A) Continuous
- B) Discrete
- C) Nominal
- D) Ordinal
- What makes stratified sampling more accurate than simple random sampling?
- A) Simpler to conduct
- B) Greater randomness
- C) Ensures representation from all subgroups
- D) Larger samples
- What causes sampling bias?
- A) Asking personal questions
- B) Selecting based on convenience
- C) Using stratified method
- D) Using a random generator
- In surveys, closed questions are preferred when:
- A) Rich data is needed
- B) Time is limited
- C) Personal insights are required
- D) Opinions need depth
- The word “quantitative” refers to:
- A) Categories
- B) Words
- C) Descriptions
- D) Numbers
- A variable that can only take specific values is called:
- A) Categorical
- B) Continuous
- C) Discrete
- D) Qualitative
- Which of the following is a categorical variable?
- A) Blood type
- B) Speed in km/h
- C) Mass in kg
- D) Length of rope
- A sample is representative only if:
- A) It is very large
- B) It reflects the characteristics of the population
- C) It’s drawn from volunteers
- D) It uses only closed questions
- One key feature of stratified sampling is:
- A) High cost
- B) Ignoring subgroups
- C) Randomly selecting within categories
- D) Total enumeration
- Why is bias problematic in statistics?
- A) It increases randomness
- B) It ensures accuracy
- C) It distorts results
- D) It strengthens sampling
- Which sampling method is non-probability based?
- A) Stratified
- B) Systematic
- C) Quota
- D) Simple random
- If a sampling frame is incomplete, it most likely leads to:
- A) Increased accuracy
- B) Reduced data volume
- C) Sampling bias
- D) Continuous variables
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
Marking Key and Full Explanations
Topic: 1. Data and its Collection – O Level Statistics 4040
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
- C) Simple Random Sampling
- ✅ Each member has an equal and independent chance.
- ❌ A, B, D may introduce bias due to selection methods.
- B) Stratified Sampling
- ✅ Divides population into subgroups and samples from each.
- ❌ A, C do not ensure proportional representation.
- C) Systematic
- ✅ Every kth individual is chosen after a random start.
- ❌ A, B, D do not follow fixed intervals.
- D) Leading Question Bias
- ✅ Suggests a preferred answer, causing bias.
- ❌ A is incorrect unless response wording changes due to pressure.
- C) Smallest possible size
- ✅ Small sample may not represent population well.
- ❌ A, B, D are key for representativeness.
- C) Stratified Sampling
- ✅ Ensures each income bracket is properly represented.
- ❌ A, B, D may ignore smaller or minority groups.
- C) Eye color
- ✅ A qualitative (non-numeric) attribute.
- ❌ A, B, D are numeric and thus quantitative.
- D) Takes specific, countable values
- ✅ E.g., number of books.
- ❌ A, B refer to continuous; C is incorrect as not all discrete data is categorical.
- C) Quantitative Continuous
- ✅ Measured values within a range.
- ❌ A is non-numeric; B implies countable whole numbers.
- B) People selected do not respond
- ✅ Skews results as entire opinions are missing.
- ❌ A, C, D are different types of bias.
- B) Selects until group quotas are filled
- ✅ Based on characteristics but not random.
- ❌ A, C, D all imply some randomness.
- C) Quota Sampling
- ✅ No need for full population list.
- ❌ Others require complete sampling frame.
- B) Leading questions
- ✅ They increase bias.
- ❌ A, C, D reduce or eliminate bias.
- C) Expensive and time-consuming
- ✅ Major disadvantage of a census.
- ❌ A is false—data is more accurate in a census.
- B) Height in cm
- ✅ Can take any real number value.
- ❌ A, C, D are discrete or interval.
- C) Sampling
- ✅ Defined as selecting part of the population.
- ❌ A, B, D refer to broader or different processes.
- B) Convenience sampling
- ✅ Highly biased due to easy access.
- ❌ A, C, D are probability-based and more reliable.
- C) Convenience sample
- ✅ Based on availability.
- ❌ A, B, D require structure or rules.
- C) To reduce bias
- ✅ Random numbers ensure fairness.
- ❌ A, B, D are incorrect reasons.
- A) The group we draw a sample from
- ✅ The population is the entire group under study.
- ❌ B, C, D are subcategories or outcomes.
- C) How old are you?
- ✅ Limited, defined numeric response.
- ❌ Others are open-ended or descriptive.
- B) Allows respondents to elaborate
- ✅ Open questions seek explanation.
- ❌ A, C, D apply to closed questions.
- C) Sample only examines part of population
- ✅ Main difference from census.
- ❌ A, B, D are secondary consequences.
- A) Continuous
- ✅ Measured data like height.
- ❌ B is countable; C/D are categorical.
- C) Ensures representation from all subgroups
- ✅ Increases accuracy over pure randomness.
- ❌ Others don’t explain its advantage.
- B) Selecting based on convenience
- ✅ Skews population representation.
- ❌ A is response bias; C/D are random methods.
- B) Time is limited
- ✅ Closed questions save time.
- ❌ A, C, D require more detailed responses.
- D) Numbers
- ✅ Quantitative = measurable/countable.
- ❌ A–C describe qualitative data.
- C) Discrete
- ✅ Specific values, often integers.
- ❌ A, B, D are other variable types.
- A) Blood type
- ✅ Categorical: A, B, AB, O.
- ❌ Others are continuous or measurable.
- B) It reflects the characteristics of the population
- ✅ Essential for representation.
- ❌ A, C, D don’t ensure representativeness.
- C) Randomly selecting within categories
- ✅ Strata ensures proportional sampling.
- ❌ A, B, D are incorrect.
- C) It distorts results
- ✅ Leads to incorrect conclusions.
- ❌ A, B, D are false or irrelevant.
- C) Quota
- ✅ Researcher chooses based on category, not random.
- ❌ A, B, D are probability-based.
- C) Sampling bias
- ✅ Frame does not include full population.
- ❌ A, B, D are unrelated effects.
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