Data Collection and Sampling

Population

The whole set of items or individuals that are of interest.

Raw data

Data that has been collected but has not yet been processed.

Census

A data collection method where every member of the population is measured or observed.

Advantage of a census

The results should be completely accurate because every member of the population is included.

Disadvantages of a census

It is time-consuming and expensive.

Sample

A subset of the population used to collect data.

Advantages of using a sample

It is cheaper and less time-consuming than a census, and there is less data to process.

Disadvantage of using a sample

The data may not be as accurate as a census because the sample may be too small, biased or not representative.

Sampling unit

An individual member or item of the population.

Sampling frame

A list of all the sampling units in the population.

Random sampling

A sampling method where chance is used to select members of the population.

Simple random sample

A sample of size n where every possible sample of size n has an equal chance of being selected.

How to carry out simple random sampling

Number each member of the population and use random numbers to select the required sample.

Advantages of simple random sampling

It is free from bias, easy to use and cheap.

Disadvantages of simple random sampling

It is not suitable for large samples and a sampling frame is needed.

Systematic sampling

A sampling method where the required elements are chosen at regular intervals from an ordered list.

How to carry out systematic sampling

Choose a starting point and then select every kth member from the sampling frame.

Advantages of systematic sampling

It is simple, quick to use and suitable for large samples.

Disadvantages of systematic sampling

A sampling frame is needed and bias can be introduced if there is a pattern in the sampling frame.

Stratified sampling

A sampling method where the population is divided into mutually exclusive strata and a random sample is taken from each stratum.

How to carry out stratified sampling

Divide the population into strata, work out how many are needed from each stratum in proportion to the population, then randomly sample within each stratum.

Advantage of stratified sampling

The sample should accurately reflect the population because each stratum is represented in proportion to its size.

Disadvantage of stratified sampling

The population must be clearly classified into distinct strata, which can be time-consuming.

Non-random sampling

A sampling method where chance is not used to select the sample.

Quota sampling

A non-random sampling method where the population is divided into groups or categories and a fixed number is selected from each group until each quota is full.

How to carry out quota sampling

Divide the population into suitable groups or categories, decide the quota needed from each group, then select people or items until each quota is filled.

Quota sampling exam trap

Do not describe the selection as random because quota sampling is a non-random sampling method.

Advantages of quota sampling

No sampling frame is needed, and it can be quick, cheap and efficient.

Disadvantages of quota sampling

It can introduce bias because the researcher chooses who to include within each group, and dividing the population into groups can be time-consuming.

Opportunity sampling

A non-random sampling method where the sample is taken from people or items that are available at the time of the study and fit the required criteria.

Advantages of opportunity sampling

It is easy to carry out and cheap.

Disadvantage of opportunity sampling

It is unlikely to produce a representative sample.

Quantitative data

Data associated with numerical observations.

Qualitative data

Data associated with non-numerical observations.

Continuous variable

A variable that can take any value in a given range.

Discrete variable

A variable that can only take specific values.

Representative sample

A sample that reflects the characteristics of the population.

Bias

A systematic tendency for a sample or method to over-represent or under-represent part of the population.

Scatter diagram compatibility wording

When commenting on a scatter diagram, say the data is compatible with or supports a suggestion if the overall trend matches it. Do not say the suggestion is definitely “correct” or “proven”, because correlation only shows a general relationship.

Example: if a scatter diagram shows negative correlation between surname length and first-name length, then the data is compatible with the suggestion that children with longer surnames tend to have shorter first names.

Scatter diagram exceptions trap

A few points that do not follow the pattern do not disprove a correlation. Comment on the overall trend, not individual exceptions.

Example: even if some children with long surnames also have long first names, the data can still support Marc’s suggestion if the overall trend is negative.

When data has outliers or skewness, which summary statistics should you use?

Use median and IQR, because they are less affected by extreme values.
Avoid mean and standard deviation, because outliers/skewness can distort them.

If some values in a data set are decreased, what can happen to the median and upper quartile?

The median and upper quartile may decrease if the changed values move below the old median or old upper quartile.

This means more values are now below the old Q2Q_2Q2​ or Q3Q_3Q3​, so the position of the median or upper quartile shifts down.

Example:
If several values above 40 are decreased to below 40, then the old median may no longer have enough values below it, so the median decreases.

Key trap:
Do not say the median increases just because there are “more values below it”. More values below the old median means the median must move down, not up.