Edexcel A Level Maths - Statistics
GRADE A+ SOLUTIONS
Linear Regression
y = axⁿ
logy = loga + nlogx
Exponential Regression
y = ab^x
logy = loga + xlogb
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Brainpower
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Normal Approximation
µ = np
σ =√(np(1-p))
Mean
∑x ÷ n
GF: ∑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 trials
2 possible outcomes
Outcomes are independent
Fixed probability of success
Probability: Independent if...
P(A∩B) = P(A) X P(B)
P(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 success
r = number of times you want success
n= 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 need
Multiply along each branch
Add the results of each branch needed.
Make sure that you include enough working to show which branches you
are using (method).
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