Population & Sampling (Edexcel IGCSE Maths)

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 usually count or measure something

  • For example: the number of pets that a student has

• Discrete data is quantitative data that takes specific numerical values

  • These may or may not be integers

    • For example: number of pets, shoe sizes, ...

  • The values could go on forever

    • 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 an interval

    • For example: the height of a student

  • Continuous data is often presented as rounded values

    • to the level of precision of whatever measured them

• 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 grouped data?

• Discrete 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

• Continuous data can be grouped into class intervals

  • The class intervals must have no gaps between them

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

  • You can use a combination of $<,>,\leq,\geq$ to achieve this

    • E.g. for height, $h$ cm, the intervals could be $0\leq h<80$, $80\leq h<160$, $160\leq h<200$

• 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

  • e.g. if an IT expert wanted to investigate the speed of mobile phones in the UK

    • The population is all the phones in the UK

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

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.

(a) State the population in this situation.

Answer:

Final answer: The population is the 600 mice living in the enclosure

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

Answer:

Final answer: 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

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

Answer:

Final answer: Mike should increase the sample size to increase the reliability of the results