statistics

• linear interpolation with raw data

  • to find the position of your median, halve the total number of values and add 0.5
  • to find the position of the quartiles, round up for a decimal, or add 0.5 for an integer
• linear interpolation for grouped data

  1. position of your median (P) = n/2
  2. continuity correction (e.g. if they’re 11-20 and 21-30, you’ll have to change them to their unrounded values)
  3. find the class that contains P
  4. create a number line, with the values of the top (A) and bottom (B) of the class at either end and the median, labelled M, in the middle
  5. underneath the number line, add the cumulative frequencies for the top (C) and bottom (D) of the class, and the value P under the label M
  6. form an equation where:(M - A)/(B - A) = (P - C)/(D - C)and solve
• simple random sampling

  1. assign everyone a number
  2. generate random numbers
  3. choose the people with the corresponding numbers

  pros:

  • bias-free
  • easy and cheap

  cons:

  • not suitable for large population
  • requires sampling frame
• systematic sampling

  1. pick a number ‘n’
  2. select every nth person in the sampling frame

  pros:

  • simple and quick
  • suitable for larger populations

  cons:

  • can introduce bias if sampling frame is not random
  • requires sampling frame
• stratified sampling

  1. split into groups based on a factor, e.g. race
  2. assign a number to each person
  3. sample each group in proportion to the percentage of the population they take up

  pros:

  • guarantees proportionate representation of the population
  • reflects the population accurately

  cons:

  • time consuming
  • requires sampling frame
  • population needs to have easily divisible groups
• quota sampling

  1. split into groups
  2. find people that satisfy those groups (e.g. 50 men and 50 women at a shopping centre)
  3. doesn’t matter how those people are found

  pros:

  • quick, easy and cheap
  • no sampling frame
  • groups make it representative of the population

  cons:

  • easily biased
  • a lot of people won’t respond
• opportunity sampling

  1. sample taken based on who ever is available at the time
  2. keep going until you reach the desired number of responses

  pros:

  • quick, easy and cheap
  • no sampling frame

  cons:

  • easily biased
  • a lot of people won’t respond
  • unlikely to be representative