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school.","correct":false,"explanation":"This includes students from other year groups, making it broader than the group being investigated. The population is Year 12 students in that school."},{"text":"Year 12 students in every school.","correct":false,"explanation":"This extends the group beyond the specified school. As the survey concerns one school, the population is Year 12 students in that school."},{"text":"Teachers of Year 12 in that school.","correct":false,"explanation":"This confuses people connected with the students with the group being studied. The population is the Year 12 students themselves in that school."}]},{"id":"c1078474-e7f4-4fc5-b18d-23ce8f4d9e9d","cardType":"basic","points":1,"front":"A principal asks every student in a college about a timetable. What method is this?","back":"Census.","mcqOptions":[{"text":"Census.","correct":true,"explanation":"A census collects information from every member of the population. Since every college student is asked, the principal is carrying out a census."},{"text":"Simple random sample.","correct":false,"explanation":"Simple random sampling selects only some individuals, each with an equal chance of selection. Asking every college student makes this a census instead."},{"text":"Systematic sample.","correct":false,"explanation":"Systematic sampling selects individuals at regular intervals from an ordered list. Here nobody is omitted, so the method is a census."},{"text":"Stratified sample.","correct":false,"explanation":"Stratified sampling selects proportional samples from defined subgroups. Because the principal asks every student rather than selecting some, this is a census."}]},{"id":"037ad630-d47b-4328-82ba-6220d60d512d","cardType":"basic","points":1,"front":"If some groups are systematically more likely to be selected, what problem is present?","back":"Bias.","mcqOptions":[{"text":"Bias.","correct":true,"explanation":"Bias occurs when the selection process systematically favours some groups over others, making the sample less representative of the population."},{"text":"Random variation.","correct":false,"explanation":"Random variation produces differences by chance rather than through systematic favouring. Groups being consistently more likely to be selected indicates bias."},{"text":"Sampling error.","correct":false,"explanation":"Sampling error is the chance difference between a sample result and the true population value. Systematically unequal selection probabilities create bias instead."},{"text":"Census.","correct":false,"explanation":"A census collects data from every member of the population, so there is no selection of only certain groups. Systematic over-selection is bias."}]},{"id":"6a0e46de-146f-4f3a-9d62-482de08e2a7a","cardType":"cloze","points":null,"front":"A sample is chosen from the [ ] and used to draw conclusions about that larger group.","back":"A sample is chosen from the population and used to draw conclusions about that larger group.","mcqOptions":[{"text":"population","correct":true,"explanation":"The population is the complete group of interest. A sample is a smaller subset selected from it and used to make conclusions about it."},{"text":"sample","correct":false,"explanation":"This would incorrectly say that a sample is chosen from itself. A sample is selected from the population, which is the larger group of interest."},{"text":"parameter","correct":false,"explanation":"A parameter is a numerical feature of a population, such as its mean, not a group from which individuals are chosen. The missing term is population."},{"text":"statistic","correct":false,"explanation":"A statistic is a value calculated from sample data rather than the larger group being studied. A sample is chosen from the population."}]},{"id":"5b6f4329-d9be-4d57-8495-c76b806e09cf","cardType":"basic","points":1,"front":"For a gym surveying active members, what is a suitable sampling frame?","back":"An up-to-date list of active members.","mcqOptions":[{"text":"An up-to-date list of active members.","correct":true,"explanation":"A suitable sampling frame lists the members of the target population accurately. A current list of active members closely matches the group the gym wishes to survey."},{"text":"An out-of-date list of former members.","correct":false,"explanation":"This frame would include people who are no longer active and may omit newer members. An up-to-date list of active members is suitable."},{"text":"An up-to-date list of all local residents.","correct":false,"explanation":"Local residents are not necessarily active gym members, so this list does not match the target population. The frame should list current active members."},{"text":"An up-to-date list of weekday visitors.","correct":false,"explanation":"This creates undercoverage by excluding active members who visit only at weekends. A suitable frame is an up-to-date list of all active members."}]},{"id":"8fb9f801-ae64-4196-897b-f25375b1c3f2","cardType":"basic","points":1,"front":"In a sports centre membership database, what are the sampling units?","back":"The individual members.","mcqOptions":[{"text":"The individual members.","correct":true,"explanation":"Sampling units are the individual objects or people selected from the sampling frame. In a membership database, these units are the individual members."},{"text":"The membership fees.","correct":false,"explanation":"Membership fees are recorded variables or payments, not the people available for selection. The sampling units are the individual members in the database."},{"text":"The membership categories.","correct":false,"explanation":"Categories classify members but are not the individual units selected for a sample. The sampling units are the individual members within those categories."},{"text":"The sports centre staff.","correct":false,"explanation":"Staff are a different group and are not the units listed in the membership population. The sampling units are the individual members."}]},{"id":"8c5157d6-609a-4dd6-b02f-d0a316e165e4","cardType":"cloze","points":null,"front":"A sampling frame should match the [ ] as closely as possible.","back":"A sampling frame should match the population as closely as possible.","mcqOptions":[{"text":"population","correct":true,"explanation":"A sampling frame should provide an accurate list of the population being studied, with as little undercoverage, duplication or inclusion of ineligible units as possible."},{"text":"sample","correct":false,"explanation":"The sample is selected using the frame, so the frame is not designed merely to match the resulting sample. It should match the population."},{"text":"statistic","correct":false,"explanation":"A statistic is a numerical summary calculated from sample data, not a group that can be listed. A sampling frame should match the population."},{"text":"census","correct":false,"explanation":"A census is a method of collecting data from every population member, not the target group itself. The sampling frame should match the population."}]},{"id":"f0747086-78b4-4575-a913-697294fcd988","cardType":"basic","points":1,"front":"A computer selects donor numbers at random from a list. What sampling method is this?","back":"Simple random sampling.","mcqOptions":[{"text":"Simple random sampling.","correct":true,"explanation":"Selecting donor numbers randomly gives each listed donor an equal chance of selection, which is the defining feature of simple random sampling."},{"text":"Systematic random sampling.","correct":false,"explanation":"Systematic sampling chooses units at fixed intervals after a random starting point. Randomly selecting donor numbers without an interval is simple random sampling."},{"text":"Stratified random sampling.","correct":false,"explanation":"Stratified sampling first divides donors into relevant groups and samples from each group. No such grouping occurs here, so this is simple random sampling."},{"text":"Quota sampling.","correct":false,"explanation":"Quota sampling fills predetermined category totals using non-random selection. A computer choosing donor numbers randomly from a list performs simple random sampling."}]},{"id":"cea2cbdb-5b1f-463b-9421-2608745821da","cardType":"cloze","points":null,"front":"In simple random sampling, every member has an [ ] of being selected.","back":"In simple random sampling, every member has an equal chance of being selected.","mcqOptions":[{"text":"equal chance","correct":true,"explanation":"Simple random sampling gives each population member the same opportunity of selection, so no individual is favoured by the sampling method."},{"text":"different chance","correct":false,"explanation":"Giving members different opportunities would favour some individuals and make the method non-random. The correct term is “equal chance”, because selection should not depend on membership characteristics."},{"text":"unequal chance","correct":false,"explanation":"Unequal opportunities create selection bias, since some members are more likely to enter the sample. Simple random sampling requires “equal chance” for every member."},{"text":"greater chance","correct":false,"explanation":"A greater opportunity for some members would make the sample systematically favour them. The defining condition is “equal chance” for every member of the population."}]},{"id":"c72b1cb1-d494-4ce8-8e1f-dbf4d38f1a67","cardType":"basic","points":1,"front":"What must be complete for simple random sampling to be relatively unbiased?","back":"The sampling frame.","mcqOptions":[{"text":"The sampling frame.","correct":true,"explanation":"A complete sampling frame lists every member of the target population, allowing each person to have an equal opportunity of selection and reducing coverage bias."},{"text":"The target population.","correct":false,"explanation":"The target population is the group being studied, not the list used to select individuals. The correct requirement is a complete sampling frame containing every population member."},{"text":"The sample size.","correct":false,"explanation":"A suitable sample size affects reliability, but it does not ensure that everyone can be selected. The sampling frame must be complete to avoid excluding parts of the population."},{"text":"The questionnaire.","correct":false,"explanation":"A questionnaire records responses after selection and does not determine who can be chosen. Unbiased selection depends on having a complete sampling frame."}]},{"id":"27c491a2-23ce-4659-8c8a-e3629246333a","cardType":"basic","points":1,"front":"What can still happen by chance in a simple random sample?","back":"Some groups may be under-represented.","mcqOptions":[{"text":"Some groups may be under-represented.","correct":true,"explanation":"Random selection can produce a sample whose group proportions differ from those in the population. A group may therefore appear less often than its population proportion by chance."},{"text":"All groups will be represented proportionally.","correct":false,"explanation":"Simple random sampling does not guarantee exact population proportions; random variation can make some groups appear less or more often. The correct possibility is that some groups may be under-represented."},{"text":"The sample will always match the population.","correct":false,"explanation":"A random sample is intended to reflect the population, but it cannot guarantee a perfect match. Chance variation means some groups may be under-represented."},{"text":"Every group will be equally represented.","correct":false,"explanation":"Groups may have different population sizes, and random selection does not force equal numbers from each group. The relevant chance outcome is that some groups may be under-represented."}]},{"id":"67d7b76c-9f4e-4824-b8b6-eb6f8a3990e7","cardType":"basic","points":1,"front":"A teacher chooses every 6th name from an ordered list. What sampling method is this?","back":"Systematic sampling.","mcqOptions":[{"text":"Systematic sampling.","correct":true,"explanation":"Systematic sampling selects individuals at a fixed interval from an ordered list. Choosing every sixth name is therefore a systematic procedure."},{"text":"Stratified sampling.","correct":false,"explanation":"Stratified sampling divides the population into groups and samples from each in proportion to its size. Taking every sixth name from one list uses a fixed interval instead."},{"text":"Quota sampling.","correct":false,"explanation":"Quota sampling fills chosen category totals, usually without random selection within categories. A fixed step through an ordered list is systematic sampling."},{"text":"Cluster sampling.","correct":false,"explanation":"Cluster sampling selects whole groups or clusters rather than every fixed-numbered individual. Selecting every sixth name is systematic sampling."}]},{"id":"40cd5d94-4e59-41e7-b062-9fb79c7a2377","cardType":"cloze","points":null,"front":"Systematic sampling selects at [ ] from an [ ].","back":"Systematic sampling selects at regular intervals from an ordered list.","mcqOptions":[{"text":"Systematic sampling selects at regular intervals from an ordered list.","correct":true,"explanation":"The defining procedure is to choose every kth member, or another fixed step, while moving through a list whose members have been put into an order."},{"text":"Systematic sampling selects at random intervals from an ordered list.","correct":false,"explanation":"The list is appropriate, but changing the step randomly is not systematic sampling. The interval must be regular, such as selecting every fifth member."},{"text":"Systematic sampling selects at regular intervals from a random list.","correct":false,"explanation":"A fixed interval is required, but the list must provide an order through which selection proceeds. The correct description uses an ordered list."},{"text":"Systematic sampling selects at equal proportions from an unordered list.","correct":false,"explanation":"Systematic sampling does not select proportions from an unordered collection. It uses regular intervals through an ordered list."}]},{"id":"ef05b880-c039-48d2-bba9-44c94ef20e5d","cardType":"basic","points":1,"front":"When can systematic sampling become biased?","back":"When a list pattern or cycle matches the interval.","mcqOptions":[{"text":"When a list pattern or cycle matches the interval.","correct":true,"explanation":"If a repeating pattern in the ordered list has the same period as the selection interval, the sample can repeatedly favour or exclude particular types of member."},{"text":"When the sampling frame contains every member.","correct":false,"explanation":"A complete frame improves coverage and reduces bias rather than causing it. Bias can arise when a repeating list pattern aligns with the selection interval."},{"text":"When the sample is selected without replacement.","correct":false,"explanation":"Selecting without replacement is normal for many samples and does not create this specific systematic bias. The problem occurs when list periodicity matches the interval."},{"text":"When the interval is applied consistently.","correct":false,"explanation":"Consistency is what defines systematic sampling and is not itself a source of bias. Bias arises when a list pattern or cycle matches that interval."}]},{"id":"6df8b1ef-004f-4658-a093-7bdb0126e75f","cardType":"basic","points":1,"front":"The population is split into groups and proportional numbers are chosen. What method is this?","back":"Stratified sampling.","mcqOptions":[{"text":"Stratified sampling.","correct":true,"explanation":"Stratified sampling divides the population into strata and chooses numbers from each in proportion to the stratum sizes, preserving the population structure."},{"text":"Simple random sampling.","correct":false,"explanation":"Simple random sampling selects individuals directly from the whole population without deliberately allocating proportional numbers to groups. Proportional group selection is stratified sampling."},{"text":"Systematic sampling.","correct":false,"explanation":"Systematic sampling selects at a fixed interval from an ordered list. It does not necessarily divide the population into groups and sample proportionally."},{"text":"Cluster sampling.","correct":false,"explanation":"Cluster sampling selects entire groups, or clusters, rather than taking proportional numbers of individuals from every group. The described method is stratified sampling."}]},{"id":"321ab939-5af5-4185-80fd-4310c9d9eaa5","cardType":"cloze","points":null,"front":"In stratified sampling, bigger strata should contribute [ ] than smaller strata.","back":"In stratified sampling, bigger strata should contribute more people than smaller strata.","mcqOptions":[{"text":"more people","correct":true,"explanation":"Proportional allocation means a stratum’s sample size follows its population size. Therefore, a larger stratum contributes more individuals than a smaller one."},{"text":"fewer people","correct":false,"explanation":"This reverses proportional allocation: larger strata should receive larger, not smaller, sample contributions. The correct fill is “more people”."},{"text":"the same number of people","correct":false,"explanation":"Equal numbers would give small strata too much influence and large strata too little. Proportional stratified sampling requires larger strata to contribute “more people”."},{"text":"equal numbers of people","correct":false,"explanation":"Allocating equal numbers ignores differences in stratum sizes and is not proportional sampling. Larger strata should contribute “more people” than smaller strata."}]},{"id":"c67a1c6e-941a-43b2-9b8b-fdb4fc102bc3","cardType":"cloze","points":null,"front":"For stratified sampling: number from stratum = [ ] ÷ population size × [ ].","back":"For stratified sampling: number from stratum = stratum size ÷ population size × sample size.","mcqOptions":[{"text":"For stratified sampling: number from stratum = stratum size ÷ population size × sample size.","correct":true,"explanation":"The stratum’s share of the population is found using stratum size ÷ population size, then multiplied by the total sample size to allocate its representative number."},{"text":"For stratified sampling: number from stratum = sample size ÷ population size × stratum size.","correct":false,"explanation":"This reverses the two quantities, treating the sample size as the stratum numerator. The correct calculation uses stratum size ÷ population size, then multiplies by sample size."},{"text":"For stratified sampling: number from stratum = population size ÷ stratum size × sample size.","correct":false,"explanation":"The ratio has been inverted, so a smaller stratum would incorrectly receive a larger allocation. Use stratum size ÷ population size × sample size instead."},{"text":"For stratified sampling: number from stratum = stratum size ÷ sample size × population size.","correct":false,"explanation":"This uses sample size as the denominator and population size as the multiplier, reversing the allocation formula. The correct multiplier is sample size, after dividing by population size."}]},{"id":"89065eef-b4e1-4231-be16-2f2b1939bfe6","cardType":"basic","points":2,"front":"A school has 640 pupils, 72 in a stratum, and wants a sample of 50. How many from that stratum?","back":"$$\\frac{72}{640}\\times 50=5.625$, so 6.","mcqOptions":[{"text":"$$\\frac{72}{640}\\times 50=5.625$, so 6.","correct":true,"explanation":"The proportional allocation is 5.625 pupils. Since a sample must contain a whole number of pupils, this is rounded to 6."},{"text":"$$\\frac{72}{640}\\times 50=5.625$, so 5.","correct":false,"explanation":"Truncating the decimal instead of rounding gives 5, but 5.625 rounds to 6 because the decimal part is at least 0.5."},{"text":"$$\\frac{72}{640}\\times 50=5.625$, so 7.","correct":false,"explanation":"Rounding 5.625 to the next whole number gives 6, not 7. The extra increase would over-allocate this stratum beyond the nearest proportional sample size."},{"text":"$$\\frac{72}{640}\\times 50=5.625$, so 9.","correct":false,"explanation":"This overestimates the allocation, often caused by mishandling the division before multiplying. The proportional calculation gives 5.625, which rounds to 6 pupils."}]},{"id":"2b1243c5-33a1-42d6-8495-419886f8f0ad","cardType":"basic","points":1,"front":"A student asks pupils until he has 20 boys and 20 girls. What sampling method is this?","back":"Quota sampling.","mcqOptions":[{"text":"Quota sampling.","correct":true,"explanation":"Quota sampling involves selecting people until predetermined numbers in specified groups have been reached, here 20 boys and 20 girls."},{"text":"Stratified sampling.","correct":false,"explanation":"Stratified sampling randomly selects people from each group in proportion to its size. Stopping after fixed group totals describes quota sampling."},{"text":"Opportunity sampling.","correct":false,"explanation":"Opportunity sampling chooses people who are easiest to access, without setting category targets. Reaching fixed numbers of boys and girls is quota sampling."},{"text":"Systematic sampling.","correct":false,"explanation":"Systematic sampling selects every kth person from an ordered list or stream. Setting targets of 20 boys and 20 girls instead describes quota sampling."}]},{"id":"e26ea6ba-bdda-423d-8a55-5c2ef34b0c47","cardType":"cloze","points":null,"front":"Quota sampling fills [ ] from groups, usually without [ ] selection.","back":"Quota sampling fills fixed numbers from groups, usually without random selection.","mcqOptions":[{"text":"Quota sampling fills fixed numbers from groups, usually without random selection.","correct":true,"explanation":"Quota sampling sets a target number from each group and then selects people until each quota is filled, usually without using random selection."},{"text":"Quota sampling fills equal numbers from groups, usually without random selection.","correct":false,"explanation":"Quota sampling uses fixed target numbers, which need not be equal for every group. Replacing fixed with equal wrongly assumes all groups receive identical quotas."},{"text":"Quota sampling fills fixed numbers from groups, usually without systematic selection.","correct":false,"explanation":"The defining contrast is that quota sampling usually avoids random selection, not that it avoids systematic selection. The missing term is random."},{"text":"Quota sampling fills proportional numbers from groups, usually without stratified selection.","correct":false,"explanation":"Quotas are fixed targets and are commonly filled without random selection. Proportional numbers and stratified selection describe different sampling ideas, not this definition."}]},{"id":"a962b8c9-9795-4d91-aa71-61149cc52834","cardType":"basic","points":2,"front":"Why can quota sampling be biased?","back":"The researcher may choose convenient people.","mcqOptions":[{"text":"The researcher may choose convenient people.","correct":true,"explanation":"Quota sampling can be biased because, once a quota is needed, the researcher may choose accessible or convenient people who do not represent the whole group."},{"text":"The researcher may choose random people.","correct":false,"explanation":"Random selection generally reduces selection bias rather than causing it. Quota sampling is biased when the researcher fills quotas by choosing convenient people."},{"text":"The researcher may choose equal groups.","correct":false,"explanation":"Having equal quotas is not itself the main source of bias. The problem is that the researcher may choose convenient people rather than selecting randomly within each group."},{"text":"The researcher may choose all people.","correct":false,"explanation":"Quota sampling does not involve selecting everyone, and a census would not usually create this particular selection bias. Bias arises from choosing convenient people to fill quotas."}]},{"id":"668ff64a-3299-4f1c-a921-04c3ef68aa1f","cardType":"basic","points":1,"front":"A manager asks the first 30 gym members entering on Tuesday morning. What method is this?","back":"Opportunity sampling.","mcqOptions":[{"text":"Opportunity sampling.","correct":true,"explanation":"Opportunity sampling selects people who are readily available at the time, such as the first gym members entering on Tuesday morning."},{"text":"Quota sampling.","correct":false,"explanation":"Quota sampling continues until fixed numbers from specified groups are reached. Selecting the first 30 available members is opportunity sampling."},{"text":"Systematic sampling.","correct":false,"explanation":"Systematic sampling uses a regular interval, such as every fifth member from a list. Taking the first 30 available members is opportunity sampling."},{"text":"Stratified sampling.","correct":false,"explanation":"Stratified sampling divides the population into groups and randomly samples within them. Choosing the first available gym members uses opportunity sampling."}]},{"id":"a11e3872-08cb-4783-bd9c-8361c5d3db28","cardType":"cloze","points":null,"front":"Opportunity sampling is also called [ ].","back":"Opportunity sampling is also called convenience sampling.","mcqOptions":[{"text":"convenience sampling","correct":true,"explanation":"Opportunity sampling is another name for convenience sampling because both select participants who are easiest or most convenient for the researcher to reach."},{"text":"stratified sampling","correct":false,"explanation":"Stratified sampling divides the population into groups and samples from each, usually randomly. The alternative name for opportunity sampling is convenience sampling."},{"text":"quota sampling","correct":false,"explanation":"Quota sampling fills predetermined numbers from particular groups, whereas convenience sampling selects people who are easiest to reach. They are different methods."},{"text":"systematic sampling","correct":false,"explanation":"Systematic sampling selects participants at a regular interval from an ordered list or sequence. Opportunity sampling is instead known as convenience sampling."}]},{"id":"1b220e6b-a593-489c-82b3-6c084c7a8d7c","cardType":"basic","points":2,"front":"Why may opportunity sampling fail to represent the population?","back":"It only uses people easiest to reach.","mcqOptions":[{"text":"It only uses people easiest to reach.","correct":true,"explanation":"Opportunity samples may overrepresent people who are available in one place or at one time, because they include only those easiest for the researcher to reach."},{"text":"It only uses people chosen at random.","correct":false,"explanation":"Random selection is intended to improve representation, not cause this problem. Opportunity sampling may fail because it uses people who are easiest to reach."},{"text":"It only uses people from every group.","correct":false,"explanation":"Including people from every group would generally improve coverage, although proportions could still matter. The key weakness is selecting only those easiest to reach."},{"text":"It only uses people with equal opinions.","correct":false,"explanation":"Opportunity sampling does not deliberately select people with identical opinions. Its representativeness suffers because it relies on people who are easiest to reach."}]}]}],"examCountdown":{"examDate":"2027-05-13","paperLabel":"Paper 1"},"heading":"1.2 Sampling","title":"Sampling Flashcards","topbar":{"backHref":"/as-level/maths/edexcel/flashcards"},"topicSidebar":"$L38"}]}],"topicId":"a79e7323-1478-49da-a0e0-17697791aa82","walled":"$L39"}],"$L3a","$L3b"]

1.2 Sampling Flashcards

1.2 Sampling Flashcards