Edexcel A-level Further Mathematics 'Statistics 3 (S3)' Revision

Contains a list of all the formulae you need for the exam, as well as further notes and tips on the Edexcel specification of Statistics 3 (S3).

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Statistics 3
Formulae
2) 2
Sampling ~( , ~( ,
, )
+ ~( + , 2 2
+ 2 2
)
2 2 2 2
- ~( - , + )
() = ()()
( + ) = +
( - ) = -
( + ) = 2 2
+ 2 2
( - ) = 2 2
+ 2 2
The Normal Distribution () = ; unbiased estimator
~(, 2 )
-
=
= =
2 2 -2
= = =
-1 -1
2
~ (, )
-
=
( ) =
2 2
( ) = =
2 2
~ ( , ),
~ ( , )
( - )-( - )
=
2
2
+

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Page 2

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Goodness of Fit ( - )2
2 = =1
, > 5
~[, ]
1
( = ) = , = 1, 2, ... ,
1
= ( = ) = , = 1, 2, ... ,
= - 1
~(, )
(× )
=
×
( = ) = (
) () (1 - )- , = 0, 1, 2, ... ,
= ( = ), = 0, 1, 2, ...…read more

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×
=
= ( - 1)( - 1)
Correlation and Regression
=
= -
(6 2 )
= 1 - (2 -1)…read more

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Notes Tips
Sampling Simple random sample - A simple random sample The advantages and disadvantages of a simple
is a sample of size where every other sample of random sample are:
size has an equal chance of being selected Advantages: More accurate estimates as
Simple random sample of 15 pupils from 56 boys random process; possible to estimate
and 64 girls from a school - Label pupils between sampling errors as random process; free
1-120; select 15 different numbers between 1- from bias as random…read more

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Disadvantages: Not suitable for large
required number of students from each course populations; sampling frame required which
using a random numbers table may be difficult to construct or may not exist
Quota sample of 30 fish from an estimated 1400 for large populations; individual strata may
trout, 600 bass and 450 pike from a lake - Fish are not be clear as some strata may overlap
caught from the lake until the quota of (1400 ÷ The advantages and disadvantages of a quota
2450) ×…read more

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Know the unbiased estimator of 2 assumes that the
= () - variance of the sample is equal to the variance of the
population
~(, 2 ) Know to use the Percentage Points of the Normal
-
= Distribution table to find
= To do a test of of a normal distribution:
=
State the null hypothesis (e.g. 0 : = 5)
-2
2 = 2 = -1
= -1
and the alternative hypothesis (e.g. > 5).
State the distribution (e.g. ~(5, 0.…read more

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Know that the central limit theorem assumes that if
the sample size is large enough; then is
approximately normally distributed
2
~ ( , ),
2
~ ( , ) Know the test of of two normal distributions
( - )-( - )
assumes that and are independent random
= variables
2 2
+ To do a test of of two normal distributions:
State the null hypothesis (e.g. 0 : = )
and the alternative hypothesis (e.g. 1 : >
). State the distribution (e.g.…read more

Page 8

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Goodness of Fit ( - )2 Know to use the Percentage Points of the Chi-
2 = =1
, > 5
2
Squared Distribution table to find
Know if the is less than five, e.g. combine the last
two groups to leave five groups; degrees of freedom
is given by e.g.…read more

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If the binomial model is not suitable, then:
(× )
= Trials are not independent
×
There is not a fixed number of trials
( = ) = (
) () (1 - )- , = 0, 1, 2, ... ,
Each trial is not either success or failure
= ( = ), = 0, 1, 2, ...…read more

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To do a test whether two variables are independent
or not independent:
= ( - 1)( - 1)
State the null hypothesis (e.g. 0 : No
association between height and weight) and
the alternative hypothesis (e.g. 1 : There is
an association between height and weight)
Calculate and 2 using the formula.
2
Calculate using the formula and find
using the Percentage Points of the Chi-
Squared Distribution table
State the conclusion by rejecting the null
hypothesis if 2 is less than 2
(e.g. 5.…read more

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