Stats

• Population

  The whole set of items that are of interest
• Census


  Observes or measures every member of a population
• Sample


  A selection of observations taken from a subset of the population which is used to find out information about the population as a whole
• Sampling units


  Individual units of a population
• Sampling frame


  A list of individually named or numbered sampling units
• Simple random sample

  Every sample of size n has an equal chance of being selected
• Systematic sampling

  The required elements are chosen at regular intervals from an ordered list
• Stratified sampling

  The population is divided into mutually exclusive strata and a random sample is taken from each
• Quota sampling

  An interviewer or researcher selects a sample that reflects the characteristics of the whole population
• Opportunity sampling

  Taking the sample from people who are available at the time the study is carried out and who fit the criteria
• Quantitative variables/data

  Variables or data associated with numerical observations
• Qualitative variables/data

  Variables or 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 take only specific values in a given range
• Grouped frequency table

  The specific data values are not shown, the groups are more commonly known as classes
• Class boundaries

  The maximum and minimum values that belong in each class
• Midpoint

  The average of the class boundaries
• Class width

  The difference between the upper and lower class boundaries
• Mutually Exclusive Events


  P(AUB)=P(A)+P(B)

  P(A or B) = P(A) + P(B)
• What does Mutually exclusive events mean?

  Events that cannot occur at the same time.
• Statistically Independent Events


  P(A and B)= P(A) x P(B)
• Set Notation:

  
• Population


  The whole set of items that are of interest
• Population


  • Items manufactured by a factory
  • All the people in a town
• Raw data


  Unprocessed information
• Census


  Observes or measures every member of a population
• Sample


  A selection of observations taken from a subset of the population which is used to find out information about the population as a whole
• Advantages and disadvantages of

  • Census
  • Sample
• Sample size


  Can affect the validity of any conclusions drawn
• Sample size


  • Depends on the required accuracy and available resources
  • Generally, the larger the sample, the more accurate it is, but you will need greater resources
  • If the population is very varied, you need a larger sample than if the population were uniform
• Different samples can lead to different conclusions due to the natural variation in a population
• Sampling units


  Individual units of a population
• Sampling frame


  A list of individually named or numbered sampling units of a population
• What are the disadvantages of a census?

  Time-consuming, expensive, may destroy items, lots of data to process
• A measure of central tendency is a number we can use to represent what is going on in the centre of our data.
• What are the three measures of central tendency?

  Mean, median, mode