S1 AS/A2 Edexcel Mindmap Summary Points

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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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