Stats + Mechanics

• What is the definition of a population in statistics?

  The population is the whole set of items that are of interest.
• What is raw data in statistics?

  Raw data is the information obtained from a population.
• What does a census measure?

  A census measures or observes every member of a population.
• What is a sample in statistics?

  A sample is a selection of observations taken from a subset of the population.
• What are the advantages and disadvantages of using a census?

  Advantages:

  • Results should be completely accurate

  
  

  Disadvantages:

  • Time-consuming and expensive
  • Cannot be used when testing destroys the process
  • Hard to process large quantities of data
• What are the advantages and disadvantages of using a sample?

  Advantages:

  • Less time-consuming and cheaper
  • Fewer people have to respond
  • Less data needs to be processed

  
  

  Disadvantages:

  • Data may not be as accurate
  • Sample may not be large enough to give information about small subgroups
• What are individual units of a population called?

  Individual units of a population are known as sampling units.
• What is a sampling frame?

  A sampling frame is a list formed by naming and numbering sampling units.
• What is random sampling?

  Random sampling is when each member of the population has an equal chance of being selected.
• What is the goal of random sampling?

  The goal of random sampling is to ensure the sample is representative of the population and to remove bias.
• What are the three types of random sampling?

  1. Simple random sampling
  2. Systematic sampling
  3. Stratified sampling
• What is simple random sampling?

  A simple random sample of size \( n \) is one where every sample of size \( n \) has an equal chance of being selected.
• How can a simple random sample be taken using a calculator or random number generator?

  Number each member from 1-100 and generate 12 random numbers between 1-100.
• How can a simple random sample be taken using lottery sampling?

  Write the names of members on identical cards, place them in a hat, and draw 12 cards.
• What are the advantages and disadvantages of simple random sampling?

  Advantages:

  • Free of bias
  • Easy and cheap for small samples and populations
  • Each sampling unit has a known and equal chance of selection

  
  

  Disadvantages:

  • Not suitable for large samples and populations
  • Sampling frame needed
• What is non-random sampling?

  Non-random sampling is when samples are selected based on non-random criteria.
• What is quota sampling?


  Quota sampling is when an interviewer selects a sample that reflects the characteristics of the whole population.
• What are the advantages and disadvantages of quota sampling?

  Advantages:

  • Allows a small sample to still be representative of the population
  • No sampling frame required
  • Quick, easy, and inexpensive
  • Easy comparison between different groups within a population

  
  

  Disadvantages:

  • Non-random sampling can introduce bias
  • Population must be divided into groups, which can be costly or inaccurate
  • Increasing scope of study increases number of groups, adding time and expenses
  • Non-responses not recorded
• What is opportunity sampling?

  Opportunity sampling is when a sample is taken from people who are available at the time of study and fit the criteria.
• What are the advantages and disadvantages of opportunity sampling?

  Advantages:

  • Easy and inexpensive

  
  

  Disadvantages:

  • Unlikely to provide a representative result
  • Highly dependent on individual researcher
• What are quantitative variables?

  Quantitative variables are associated with numerical observations.
• What are qualitative variables?

  Qualitative variables are associated with non-numerical observations.
• What is a continuous variable?

  A continuous variable can take any value in a given range.
• What is a discrete variable?

  A discrete variable can only take specific values.
• What are the components of a grouped frequency table?

  • Class boundaries show the maximum and minimum values in each group or class
  • The midpoint is the average of class boundaries
  • The class width is the difference between upper and lower class boundaries
• What will be provided in an exam for calculations on large data sets?

  The relevant extract will be provided.
• What is systematic sampling?

  Systematic sampling involves choosing required elements at regular intervals from an ordered list.
• How is systematic sampling performed in the example provided?

  Every fifth person is chosen after selecting the first person at random.
• What are the advantages and disadvantages of systematic sampling?

  Advantages:

  • Simple and quick to use
  • Suitable for large samples and large populations

  
  

  Disadvantages:

  • A sampling frame is needed
  • Bias introduced if sampling frame is not random
• What is stratified sampling?

  Stratified sampling involves dividing the population into mutually exclusive strata and taking a random sample from each.
• How is the number sampled in a stratum calculated?

  Number sampled in a stratum = \(\frac{\text{number in stratum}}{\text{number in population}} \times \text{overall sample size}\)
• How can the factory manager use stratified sampling to select the sample?


  The manager calculates the number of workers needed from each age group based on the total number of workers and the overall sample size.
• What are the advantages and disadvantages of stratified sampling?

  Advantages:

  • Sample accurately reflects population structure
  • Proportional representation of group within population

  
  

  Disadvantages:

  • Population must be clearly classified into distinct strata
  • Same disadvantages as simple random sampling within each stratum
• What does a measure of central tendency describe?

  The centre of the data
• When should the mode be used as a measure of central tendency?

  When data is qualitative or quantitative with one mode or two modes (bimodal)
• Why is the mode not informative if each value occurs only once?

  Because there is no value that occurs more frequently than others
• What is the median?

  The middle value when the data values are put in order
• When is the median particularly useful?

  When there are extreme values, as they do not affect it
• How is the mean calculated?


  $\bar{x} =$$\frac{\Sigma x}{n}$
• What is the mean used for?

  Quantitative data