EDEXCEL AS Level Maths: Sampling Methods and Definitions

What is a population?

The entire group of individuals or items being considered in a statistical study.

What is a sample?

A subset of the population selected for study.

What is a sampling frame?

A list of all members of the population from which a sample is drawn.

What is simple random sampling?

A sampling method where every member of the population has an equal chance of being selected.

How to carry out simple random sampling?

Obtain a complete sampling frame, assign each member a unique number, use a random number generator or table, and select the required number of individuals.

What are the advantages of simple random sampling?

Unbiased selection method, every member has an equal chance of selection, suitable for statistical analysis using probability theory.

What are the disadvantages of simple random sampling?

Requires a complete sampling frame, time-consuming for large populations, may not be representative by chance.

What is systematic sampling?

A sampling method where elements are selected at regular intervals from an ordered list after a random start.

How to carry out systematic sampling?

Arrange the population in a list, calculate sampling interval, choose a random starting point, and select every k-th member thereafter.

How do you calculate the sampling interval

k = N/n —> k = sampling interval N = total population size n = desired sample size

What are the advantages of systematic sampling?

Simple and quick, ensures even spread across population, easier than simple random sampling for large populations.

What are the disadvantages of systematic sampling?

Can be biased if there is a repeating pattern in the list, requires an ordered sampling frame.

What is stratified sampling?

A sampling method where the population is divided into strata and a random sample is taken from each stratum in proportion to its size.

How to carry out stratified sampling?

Divide population into relevant strata, determine proportion of each stratum, calculate sample size for each stratum, and use simple random sampling within each stratum.

What is the stratified sampling formula?

(size of stratum / population size) × sample size.

What are the advantages of stratified sampling?

Ensures all groups are represented, more representative than simple random sampling, reduces variability if strata are homogeneous.

What are the disadvantages of stratified sampling?

Requires detailed population information, more complex and time-consuming.

What is quota sampling?

A non-random sampling method where the population is divided into groups and a fixed number is collected from each group.

How to carry out quota sampling?

Identify relevant groups, decide quotas for each group, and select individuals non-randomly until quotas are filled.

What are the advantages of quota sampling?

Quick and inexpensive, ensures representation of key groups, no sampling frame required.

What are the disadvantages of quota sampling?

Non-random selection introduces bias, interviewer may choose convenient participants, sampling error cannot be reliably calculated.

What is opportunity sampling?

A sampling method where individuals are selected because they are easily available.

How to carry out opportunity sampling?

Go to a location where population is accessible and select individuals who are easiest to approach.

What are the advantages of opportunity sampling?

Very quick and convenient, cheap to carry out, useful for pilot studies.

What are the disadvantages of opportunity sampling?

Highly biased, unrepresentative of population, may overrepresent certain groups.

What is volunteer sampling?

A sampling method where participants self-select to take part in the study.

How to carry out volunteer sampling?

Advertise the study and allow individuals to choose to participate.

What are the advantages of volunteer sampling?

Easy to organise, participants are willing, low cost and quick.

What are the disadvantages of volunteer sampling?

Volunteer bias, sample may not represent population, people with strong opinions more likely to respond.

What is bias?

Bias occurs when a sample is not representative because some members of the population are more likely to be selected than others.

What is a representative sample?

A sample that reflects the characteristics of the population.

Why is a large sample size useful?

Reduces effect of anomalies, more reliable results, more likely to be representative.

Why is a sampling frame important?

It ensures that all members of the population have a chance of being selected.

Which sampling methods are random?

Simple random sampling, systematic sampling (after random start), stratified sampling (when random selection is used within strata).

Which sampling methods are non-random?

Quota sampling, opportunity sampling, volunteer sampling.

Which sampling method is usually most representative?

Stratified sampling, because it ensures proportional representation of all groups.

Which sampling methods do NOT require a sampling frame?

Quota sampling, opportunity sampling, volunteer sampling.

What is a key exam point for opportunity sampling?

May be biased because selection is based on convenience.

What is a key exam point for volunteer sampling?

May be biased because volunteers are self-selected.

What is a key exam point for systematic sampling?

May be biased if there is a periodic pattern in the ordered list.

What is a key exam point for quota sampling?

May be biased because selection within groups is non-random.

What is a key exam point for simple random sampling?

May not be representative due to chance variation.

What is a key exam point for stratified sampling?

Requires accurate population information and correct stratification.

Explain what you understand by a random sample from a finite population

Each sample has an equal chance of being selected

Give an example of a scenario where it is not possible to take a random sample

When you cannot create a sampling frame