AQA A Level Maths: Statistics复习笔记1.1.1 Sampling & Data Collection

What are the different types of data?

• 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 other key words do I need to know?

• The population refers to the whole set of things which you are interested in
  • For example: if a vet wanted to know how long a typical French bulldog slept for in a day then the population would be all the French bulldogs in the world
• A sample refers to a subset of the population which is used to collect data from
  • For example: the vet might take a sample of French bulldogs from different cities and record how long they sleep in a day
• A sampling frame is a list of all members of the population
  • For example: a list of employees’ names within a company
• A population parameter is a numerical value which describes a characteristic of the population
  • These are usually unknown
  • For example: the mean height of all 16-year-olds in the UK
• A sample statistic is a value computed using data from the sample
  • These are used to estimate population parameters
  • For example: the mean height of 200 16-year-olds from randomly selected cities in the UK

What are the differences between a census and sampling?

• A census collects data about all the members of a population
  • For example: the Government in England does a national census every 10 years to collect data about every person living in England at the time
• The main advantage of a census is that it gives fully accurate results
• The disadvantages of a census are:
  • It is time consuming and expensive to carry out
  • It can destroy or use up all the members of a population when they are consumables (imagine a company testing every single firework)
• Sampling is used to collect data from a subset of the population
• The advantages of sampling are:
  • It is quicker and cheaper than a census
  • It leads to less data needing to be analysed
• The disadvantages of sampling are:
  • It might not represent the population accurately
  • It could introduce bias

What sampling techniques do I need to know?Sampling Critique

When should each sampling technique be used or avoided?

• Simple random sampling: this should be used when you want a random sample to avoid bias
  • Useful when you have a small population or want a small sample (such as children in a class)
  • This can not be used if it is not possible to number or list all the members of the population (such as fish in a lake)
• Systematic sampling: this should be used when you want a random sample from a large population
  • Useful when there is a natural order (such as a list of names or a conveyor belt of items)
  • In order for the sample to be random the sampling frame needs to be random
  • This can not be used if it is not possible to number or list all the members of the population (such as penguins in Antarctica)
• Stratified sampling: this should be used when the population can be split into obvious groups of members (where members within a group have a common characteristic)
  • Useful when there are very different groups of members within a population
  • The sample will be representative of the population structure
  • The members selected from each stratum are chosen randomly
  • This can not be used if the population can not be split into groups or if the groups overlap
• Quota sampling: this should be used when a small sample is needed to be representative of the population structure
  • Useful when collecting data by asking people who walk past you in a public place or when a sampling frame is not available
  • This can introduce bias as some members of the population might choose not to be included in the sample
• Opportunity (convenience) sampling: this should be used when a sample is needed quickly
  • Useful when a list of the population is not possible
  • This is unlikely to be representative of the population structure

What are the main criticisms of sampling techniques?

• Most sampling techniques can be improved by taking a larger sample
• Sampling can introduce bias - so you want to minimise the bias within a sample
  • To minimise bias the sample should be random
• A sample only gives information about those members
  • Different samples may lead to different conclusions about the population