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).

Pages in this set

Page 1

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Statistics 3
Formulae Sampling · X~N(
x

,
x 2), Y~N(
y

,
y 2)

· aX + bY~N(a
x

,a2
x 2 + b2
y 2)

· aX - bY~N(a
x

+ b
y - b
y

,a2
x 2 + b2
y 2)

· E(XY) = E(X)E(Y)
·…

Page 2

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· Var(aX - bY) = a2
x 2 + b2
y2

The Normal Distribution · E(T) = ; unbiased estimator
· X~N(,2)
·Z=
X-

· = X =
x n

· 2 = S2 =
-nX2 n-1

· X~N(,
S
xx n-1

=
X
i

n
2

)
·Z=
X-…

Page 3

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,

nx2

), Y~N(
y

,

n
y2

)
·Z=
(X-Y)-(
x
-
y
)

nx 2 x
+
ny 2 y

Page 4

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· · x 2z
± n

z
; n

confidence ; confidence interval interval
width
Goodness of Fit
· X2 =
n i=1
(O
i
-E
)2 E
i
i

,E
i

>5
· X~U[, ]
· P(X = x
r

)=
1k

, r = 1,2,...,k
·E
i

=…

Page 5

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·p=
(n×O
i
) n×N

· P(X = x
r
np

)(p)x(1 - p)n-x, r = 0,1,2,...,n
·E
i

)=(
= P(X = x
r

)N, r = 0,1,2,...,k
· v = n - 1; if p is not estimated
· v = n - 2; if p is estimated…

Page 6

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n-1 S
xx

=
X
i
-nX2 n-1

· P(a < X < b) = P(
a-

b-

)
·E
i

= P(a < X < b)N

Page 7

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· v = n - 1; if neither nor 2 are estimated
· v = n - 2; if either or 2 is estimated
· v = n - 3; if both and 2 are estimated
· X~U[, ]
· P(a < X < b) =
- b-a

·E
i…

Page 8

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Notes Tips Sampling · Simple random sample - A simple random sample is a sample of size n
where every other sample of size n has an equal chance of being selected
· Simple random sample of 15 pupils from 56 boys and 64 girls from a school - Label…

Page 9

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enrolled in to obtain a sampling frame; select required number of students from each course
using a random numbers table
· Quota sample of 30 fish from an estimated 1400 trout, 600 bass and 450 pike from a lake -
Fish are caught from the lake until the quota of…

Page 10

Preview of page 10
+X
2

~N(
1

+
2

,
12+
2 2)

· aX - bY~N(a
x

+ b
y - b
y

,a2
x 2 + b2
y 2)

· E(XY) = E(X)E(Y)
· E(aX + bY) = a
x

+ b
y

· E(aX - bY) = a
x

-…

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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).

Pages in this set

Page 1

Preview of page 1
Statistics 3
Formulae Sampling · X~N(
x

,
x 2), Y~N(
y

,
y 2)

· aX + bY~N(a
x

,a2
x 2 + b2
y 2)

· aX - bY~N(a
x

+ b
y - b
y

,a2
x 2 + b2
y 2)

· E(XY) = E(X)E(Y)
·…

Page 2

Preview of page 2
· Var(aX - bY) = a2
x 2 + b2
y2

The Normal Distribution · E(T) = ; unbiased estimator
· X~N(,2)
·Z=
X-

· = X =
x n

· 2 = S2 =
-nX2 n-1

· X~N(,
S
xx n-1

=
X
i

n
2

)
·Z=
X-…

Page 3

Preview of page 3
,

nx2

), Y~N(
y

,

n
y2

)
·Z=
(X-Y)-(
x
-
y
)

nx 2 x
+
ny 2 y

Page 4

Preview of page 4


· · x 2z
± n

z
; n

confidence ; confidence interval interval
width
Goodness of Fit
· X2 =
n i=1
(O
i
-E
)2 E
i
i

,E
i

>5
· X~U[, ]
· P(X = x
r

)=
1k

, r = 1,2,...,k
·E
i

=…

Page 5

Preview of page 5
·p=
(n×O
i
) n×N

· P(X = x
r
np

)(p)x(1 - p)n-x, r = 0,1,2,...,n
·E
i

)=(
= P(X = x
r

)N, r = 0,1,2,...,k
· v = n - 1; if p is not estimated
· v = n - 2; if p is estimated…

Page 6

Preview of page 6
n-1 S
xx

=
X
i
-nX2 n-1

· P(a < X < b) = P(
a-

b-

)
·E
i

= P(a < X < b)N

Page 7

Preview of page 7
· v = n - 1; if neither nor 2 are estimated
· v = n - 2; if either or 2 is estimated
· v = n - 3; if both and 2 are estimated
· X~U[, ]
· P(a < X < b) =
- b-a

·E
i…

Page 8

Preview of page 8
Notes Tips Sampling · Simple random sample - A simple random sample is a sample of size n
where every other sample of size n has an equal chance of being selected
· Simple random sample of 15 pupils from 56 boys and 64 girls from a school - Label…

Page 9

Preview of page 9
enrolled in to obtain a sampling frame; select required number of students from each course
using a random numbers table
· Quota sample of 30 fish from an estimated 1400 trout, 600 bass and 450 pike from a lake -
Fish are caught from the lake until the quota of…

Page 10

Preview of page 10
+X
2

~N(
1

+
2

,
12+
2 2)

· aX - bY~N(a
x

+ b
y - b
y

,a2
x 2 + b2
y 2)

· E(XY) = E(X)E(Y)
· E(aX + bY) = a
x

+ b
y

· E(aX - bY) = a
x

-…

Comments

No comments have yet been made