Sampling techniques; bias; discrete/continuous data practice questions.

To estimate how often adults in a city exercise, a researcher questions people leaving a fitness centre one morning. Identify the sampling method and its main weakness.

• Convenience sampling; it over-represents gym-goers
• Stratified sampling; the strata sizes are unknown
• Systematic sampling; the interval is too small
• Simple random sampling; the sample is too small

Answer: Convenience sampling; it over-represents gym-goers

Choosing whoever is easiest to reach is convenience sampling, and people at a gym are not representative of all adults, so the results are biased.

In which sampling method does every possible sample of a given size have an equal chance of being selected?

• Quota sampling
• Simple random sampling
• Convenience sampling
• Systematic sampling

Answer: Simple random sampling

Only simple random sampling gives every subset of the required size the same probability of selection; systematic sampling gives each member an equal chance but not every subset.

An interviewer is told to question the first 25 women and the first 25 men she meets in a shopping centre. State the sampling technique being used.

• Stratified sampling
• Systematic sampling
• Quota sampling
• Simple random sampling

Answer: Quota sampling

Filling fixed group targets with non-random selection is quota sampling; unlike stratified sampling, the individuals are not chosen randomly.

Which of the following variables is continuous?

• The number of pets in a household
• The shoe size of a student
• The number of cars passing a junction per hour
• The time taken to complete a puzzle

Answer: The time taken to complete a puzzle

Time can take any value in an interval, so it is continuous; counts and shoe sizes only take specific separated values.

A systematic sample of 40 is taken from a numbered list of 800 employees. The first employee selected is number 7. Determine the number of the second employee selected.

• 17
• 27
• 40
• 47

Answer: 27

The sampling interval is 800 ÷ 40 = 20, so after employee 7 the next selected is 7 + 20 = 27.

A pollster is told to interview exactly 30 men and 30 women in a shopping centre, questioning whoever is available until each count is reached. Which feature prevents this from being a stratified sample?

• The people within each group are not selected at random
• The two chosen groups happen to be exactly the same size
• The total sample is far too small to count as stratified
• Men and women do not form two separate groups of people

Answer: The people within each group are not selected at random

This is quota sampling: the group sizes are fixed, but selection within each group is by convenience. Stratified sampling requires a random draw inside every stratum — the group quotas alone do not make a sample stratified.