# S1 AS/A2 Edexcel Mindmap Summary Points

- Created by: Charliewortley
- Created on: 15-05-14 14:03

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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

- y=a+bx
- Chapter 6 (Correlation)
- Sxx= [?x2- (?x)2/n]
- Syy= [?y2 - (?x)2/n]
- Sxy= [?xy - (?x?y)/n]

- Syy= [?y2 - (?x)2/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

- Sxx= [?x2- (?x)2/n]
- 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

- For Random Variable X
- 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

- Chapter 7 (Regression)

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