Population & Sampling

What are the different types of data?

Primary data is data that has been collected by the person carrying out the research
- This could be through questionnaires, surveys, experiments etc
Secondary data is data that has been collected previously
- This could be found on the internet or through other research sources
Qualitative data is data that is usually given in words not numbers to describe something
- For example: the colour of a teacher's car
Quantitative data is data that is given using numbers which counts or measures something
- For example: the number of pets that a student has
Discrete data is quantitative data that needs to be counted
- Discrete data can only take specific values from a set of (usually finite) values
- For example: the number of times a coin is flipped until a ‘tails’ is obtained
Continuous data is quantitative data that needs to be measured
- Continuous data can take any value within a range of infinite values
- For example: the height of a student
Age can be discrete or continuous depending on the context or how it is defined
- If you mean how many years old a person is then this is discrete
- If you mean how long a person has been alive then this is continuous

What is a population?

A population refers to the whole set of things which you are interested in
- e.g. if a teacher wanted to know how long pupils in year 11 at their school spent revising each week then the population would be all the year 11 pupils at the school
Population does not necessarily refer to a number of people or animals
- e.g. if an IT expert wanted to investigate the speed of mobile phones then the population would be all the different makes and models of mobile phones in the world

What is a sample?

A sample refers to a selected part (called a subset) of the population which is used to collect data from
- e.g. for the teacher investigating year 11 revision times a sample would be a certain number of pupils from year 11
A random sample is where every item in the population has an equal chance of being selected
- e.g. every pupil in year 11 would have the same chance of being selected for the teacher's sample
A biased sample is where the sample is not random
- e.g. the teacher asks pupils from just one class

What are the advantages and disadvantages of using a population?

You may see or hear the word census - this is when data is collected from every member of the whole population
The advantages of using a population
- Accurate results - as every member/item of the population is used
  - In reality it would be close to every member for practical reasons
- All options/opinions/responses will be included in the results
The disadvantages of using a population
- Time consuming to collect the data
- Expensive due to the large numbers involved
- Large amounts of data to organise and analyse

What are the advantages and disadvantages of using a sample?

The advantages of using a sample
- Quicker to collect the data
- Cheaper as not so much work involved
- Less data to organise and analyse
The disadvantages of using a sample
- A small sample size can lead to unreliable results
  - Sampling methods can usually be improved by taking a larger sample size
- A sample can introduce bias
  - particularly if the sample is not random
- A sample might not be representative of the population
  - Only a selection of options/opinions/responses might be accounted for
  - The members/items used in the sample may all have similar responses
    e.g. even with a random sample it may be possible the teacher happens to select pupils for his sample who all happen to do very little revision
It is important to recognise that different samples (from the same population) may produce different results

Worked example

Mike is a biologist studying mice and has access to 600 mice that live in an enclosure.
Mike wants to sample some of the mice for a study into their response to a new drug.
He decides to sample 10 mice, selecting those nearest to the enclosure's entrance.

State the population in this situation.

The population is the 600 mice living in the enclosure

State two possible issues with the sample method Mike intends using.

The sample size is very small - just 10 mice
The mice are not being selected at random - those nearest the entrance have a greater chance of being selected

Suggest one way in which Mike could improve the reliability of the results from his sample.

Mike should increase the sample size to increase the reliability of the results

1. Number

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5. Probability

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6. Statistics

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