a level stats

• Linear Regression


  y = axⁿ logy = loga + nlogx
• Exponential Regression

  y = ab^x logy = loga + xlogb
• Normal Approximation


  µ = npσ =√(np(1-p))
• Mean


  ∑x ÷ nGF: ∑xf ÷ ∑f
• Variance


  (∑x²/n) - (∑x/n)²
• Standard Deviation


  √variance
• Histograms: Height

  Area = k x frequency
• Frequency Density


  frequency ÷ class width
• Population


  Whole set of items of interest.
• Census


  Observes/measures every member of a population
• Sample


  Selection of observations taken from a subset of the population which is used to find out info about the population.
• Sampling Frame


  A list of individuals (named or numbered) from whom the sample is drawn
• Random Sampling


  Every member of the population has an equal chance of being selected
• Systematic Sampling


  Every nth person is chosen.
• Stratified Sampling


  Population is divided into mutually exclusive Strat and a random sample is taken from each.
• Quota Sampling


  Interviewer selects a sample that reflects the characteristics of the population
• Opportunity Sampling


  Choosing whoever is available
• Continuous Variable


  Can take any value in a given range
• Discrete Variable


  Takes specific values in a given range
• Conditions for Binomial

  Fixed no. of trials2 possible outcomesOutcomes are independent Fixed probability of success
• Probability: Independent if...


  P(A∩B) = P(A) X P(B)P(A|B) = P(A)
• Probability: Mutually exclusive if...


  P(A∩B) = 0P(A∪B) = P(A) + P(B)
• Conditional Probability


  P(A|B) = P(A∩B)/P(B)
• Probability Addition Rule


  P(A∪B) = P(A) + P(B) - P(A∩B)
• If there are 3 events, and A and B are mutually exclusive...

  P(A∪B∪C) = P(A) + P(B) + P(C) - P(A∩C) - P(B∩C)
• What is a DRV - discrete random variable


  it is a random variable that can only take certain values
• ... ...
• probability mass function


  a function that gives the probability that a discrete random variable is exactly equal to some value

  
• what does a probability distribution do


  describes the probability of any outcome in the sample space
• P(A/B) =


  (P(A n B)) ---------------P(B)
• If they are independent events P(A) * P(B) =


  P(A N B)
• SUM OF P(X=x) =


  1
• formula for probability X=r where X is the number of desired outcomes binomial distribution formula

  nCr P^r * (1-p)^(n-r)p = probability of successr = number of times you want successn= number of trials

  
• standard deviation


  a computed measure of how much scores vary around the mean score

  
• general probability addition rule


  P(A∪B)=P(A)+P(B)−P(A∩B)P(A∩B)=P(A)+P(B)−P(A∪B)
• what is an event

  a set of possible outcomes - not necessarily equally likely
• sample space

  set of all possible outcomes , all equally likely
• A ∪ B


  means A or B or both
• A ∩ B


  means both A and B
• The rules for tree diagrams are

  Select which branches you needMultiply along each branchAdd the results of each branch needed.Make sure that you include enough working to show which branches you are using (method). Be careful to allow for selection with and without replacement.if you are told what has happened for the first choice and need to find second you read off tree diagramif you are told what has happened for the second choice use formula