Population & Sampling (OCR GCSE Maths): Revision Note

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 about grouped data?

• Discrete or continuous data can be grouped into class intervals

• This is more convenient than stating every single data value

  • E.g. For house prices, you may be more interested in how many houses sold for "£200k to £250k" than exactly how many houses sold for £238k, £225k, and so on

• With continuous data, the class intervals must have no gaps between them

  • You can use a combination of to achieve this

  • E.g. for height, , the intervals could be , ,

  • The class intervals (group widths) do not necessarily need to be equal

• With discrete data the class intervals may have gaps between them, as the data can only take specific separate values

  • You still need to make it clear which group a value would go into

    • They cannot overlap

  • E.g. for "number of siblings" the groups may be "0 to 1" and "2 to 3" etc

  • Each class interval represents a small range of whole-number values, and no values exist in between them

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

• The larger the sample, the more reliable the conclusions drawn from it will be

• 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

• The larger the sample, the more reliable the conclusions drawn from it will be