# S1 AS/A2 Edexcel Mindmap Summary Points

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• S1
• 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)
• 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.
• 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 can help provide control - as in aircraft scheduling
• 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