S1 AS/A2 Edexcel Mindmap Summary Points

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Created on: 15-05-14 14:03

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- Chapter 7 (Regression)
  - y=a+bx
    - b = Sxy/Sxx
    - a = (ybar) - b(xbar)
  - Interpolation is when you estimate the value of a dependent variable within the range of data
  - Extrapolation is when you estimate a value outside the range of the data.
    - Extrapolation can be unreliable
- Chapter 6 (Correlation)
  - Sxx= [?x2- (?x)2/n]
    - Syy= [?y2 - (?x)2/n]
      - Sxy= [?xy - (?x?y)/n]
  - r = Sxy/[SqRt(SxxSyy)]
  - r is a measurement of linear relationship
    - r = 1 => perfect positive linear correlation
    - r = -1 => perfect negative correlation
    - r = 0 => no linear correlation
- Chapter 5 (Probability)
  - P(A or B or both) = P(AuB)
  - P(A and B)= P(AnB)
  - P(not A) = P(A')
  - Complementary Probability P(A')=1-P(A)
  - Addition Rule P(AuB)=P(A)+P(B)-P(AnB)
  - P(A given B) = P(A|B)
    - Conditional Probability P(A|B) = P(AuB)/P(B)
  - Multiplication Rule P(AnB) =P(A|B)xP(B)
  - A and B are independent if P(A|B)=p(A)
  - A and B are mutually exclusive if P(AnB)=0
- Chapter 4 (Representation of data)
  - A stem and leaf diagram is used to order and present data
  - A stem and leaf diagram reveals the shape of data and enables Q's to be found
  - 2 pairs of data can be compares using back to back stem and leaf diagram
  - An outlier is an extreme value. You will be told what rule to use to find outliers.
  - Box plot - Plot Q1 Q2 & Q3 Max and Min values
  - Skewness - 3(mean-median)/SD
- Chapter 3 - Representation & Summary of data (dispersion measures)
  - Range = (Highest value)-(Lowest Value)
  - Quartiles - n/4
  - Percentiles - xth percentile = xn/100 the n% to m% =Pn-Pm
  - Variance = ?x2/n - (?x/n)2
    - SD = SqRt(Var)
    - if grouped frequency replace ? with ?f
- Chapter 1 ( Mathematical Models in Statistics)
  - A mathematical model is a simplification of a real world situation.
  - Advantages
    - quick and easy to produce
    - they can simplify a more complex situation
    - they can help us improve our understanding of the real world as certain variable can readily be changed
    - they enable predictions to be made about the future
    - they can help provide control - as in aircraft scheduling
  - Disadvantages
    - they only give a partial description of the real situation
    - they only work for a restricted range of values
- Chapter 8 Discrete Random Variable
  - For Random Variable X
    - x is a particular value of X
    - P(X=x) refers to the probability that X is equal to a particular value x
  - For discrete random variable: the sum of all probabilities must add up to one or in symbols ?P(X=x) = 1
  - Cf distribution F(x)=P(X?x)
  - Expected Value of X E(X)= ?xP(X=x) =?xp(x)
  - Var(X)=E(X² )-E(X)²
  - E(aX+b)= aE(X)+b
  - Var(aX+b)= a² Var(X)
  - E(X) =(n+1)/2
  - Var(X)= [(n=1)(n-1)]/2
- Chapter 9 (Normal Distribution
  - X ? N(µ,?2)
  - if X ? N(µ,?2) and Z ? N(0,1^2) then Z=(X - µ)/?
  - ? = variance of normal distribution µ=mean

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S1 AS/A2 Edexcel Mindmap Summary Points

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