Maths u2

• population


  The whole set of items that are of interest
• sample


  A subset of the population intended to represent the population
• Sampling unit


  Individual unit of the population
• Sampling frame


  List of items of a population from which a sample is selected
• Census


  Data collected from an entire population
• Census pros and cons

  Pros

  - Completely accurate results

  
  

  Cons

  - Time consuming

  - Expensive

  - Can't be used when sampling process involves destruction

  - Large volume of data to process
• Sampling pros and cons

  Pros

  - Cheaper

  - Quicker

  - Less data to process

  
  

  Cons

  - Data may not be accurate

  - May not be large enough to represent smaller subgroups of population
• 3 types of sampling

  - Simple random

  - Systematic

  - Opportunity
• Explain simple random sampling

  1. Sampling frame created

  2. RNG generates random number corresponding to an individual unit

  3. Selected units become sample

  
  

  Every sample has equal chance of being selected
• Random sampling pros and cons

  Pros

  - Avoids bias

  - Easy

  - Cheap

  - Every unit has equal chance

  
  

  Cons

  - Chance of inaccuracy

  - Sampling frame required

  - Subgroups may not be represented
• Explain systematic sampling


  Units to be sampled are chosen at regular intervals from sampling frame

  
  

  1. Sampling frame

  2. Find k (pop/samp)

  3. Start at random value between 1 and k

  4. Sample every kth term

  5. Selected units become sample
• Systematic sampling pros and cons

  Pros

  - Simple, quick

  - Suitable for large pops

  
  

  Cons

  - Sampling frame needed

  - Can introduce bias if sampling frame isn't random
• Explain opportunity sampling


  Sample taken from people who are available at the time or who meet criteria
• Opportunity sampling pros and cons

  Pros

  - Easy to carry out

  - Inexpensive

  
  

  Cons

  - Unlikely to be representative of population

  - Dependent on individual researcher

  - Does not avoid bias
• Explain the 4 categories of data

  Categorical - Distinct categories (favourite colour)

  Numerical - Data with numbers

  Discrete - Clear intervals / only certain values

  Continuous - Measurement / No gaps
• Qualities of mean average?

  - Affected by outliers as all data is used

  - Uses every value so is representative of dataset
• Qualities of median average?

  - Not affected by outliers so better measure of central tendency

  - Does not consider all values
• Qualities of midpoint average


  - Considers skew

  - May misrepresent data set
• Qualities of Mode average


  - Not affected by outliers

  - Quick and easy

  - May misrepresent dataset
• Skew


  Measure of the distribution of data.

  Positive - Low clustered

  Negative - High clustered

  
• Binomial distribution requirements


  - Fixed number of trials

  - Two possible outcomes

  - Fixed probability of success

  - Independent trials
• Binomial formula (in booklet)

  k = r

  
• Poisson requirements


  - Independent events

  - Events occur at constant rate

  - Events occur one at a time
• Difference between binomial and poisson

  Binomial requires a given number of trials for random variable X to occur. Poisson just uses random variable given a mean
• Poisson formula


  r = x

  
• Union and intersection meaning

  Union - A or B or both (OR)

  Intersection - A and B (AND)
• Formula for union


  P(A) + P(B) - P(A and B)

  
  

  1 - P(A' and B')
• Independent events


  P(A) x P(B) = P(A and B)
• Mutually exclusive


  P(A) + P(B) = P(A or B)

  P(A and B) = 0
• Probability of exactly one event occurring

  [P(A) - P(A and B)] + [P(B) - P(A and B)]
• Subset symbol


  A c B

  
  

  "A is a subset of B"

  
• Median formula


  (n+1)/2 th value

  
  

  n is total frequency

  
• lower quartile formula


  (n+1)/4 th value
• upper quartile formula


  3(n+1)/4 th value
• Finding median/quartiles from frequency table

  - Total frequency

  - Use formula

  - Ascend group one by one

  - First x value/group to go past median value is the one

  - Same process for quartiles
• Standard deviation


  - Distance from the mean

  - Affected by outliers
• Mean of grouped frequency tables

  - Use midpoints
• Variance formula (in booklet)

  
• Does correlation imply causation

  NO
• Outlier formula