Pearson Edexcel Level 3 Advanced Subsidiary and Advanced ...
[Pages:32]Pearson Edexcel Level 3 Advanced Subsidiary and Advanced GCE in Statistics
Statistical formulae and tables
For first certification from June 2018 for: Advanced Subsidiary GCE in Statistics (8ST0)
For first certification from June 2019 for: Advanced GCE in Statistics (9ST0)
This copy is the property of Pearson. It is not to be removed from the examination room or marked in any way.
P58394A
?2017 Pearson Education Ltd. 1/1/1/1/1/1/1/
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All information in this document is correct at time of publication. ISBN 978 1 4469 4764 7 All the material in this publication is copyright ? Pearson Education Limited 2017
Contents
1 Introduction
1
2 AS Level in Statistics
2
3 A Level in Statistics
4
4 Statistical Tables
8
Table 1: Cumulative Binomial Distribution Function
8
Table 2: Cumulative Poisson Distribution Function
15
Table 3: Normal Distribution Function
17
Table 4: Percentage Points of the Normal Distribution
18
Table 5: Percentage Points of the Student's t-distribution
19
Table 6: Percentage Points of the 2 Distribution
20
Table 7: Percentage Points of the F-distribution
21
Table 8: Critical Values of the Product Moment Correlation Coefficient
23
Table 9: Critical Values of Spearman's Rank Correlation Coefficient
24
Table 10: Critical Values of the Wilcoxon Signed-Rank Statistic
25
Table 11: Critical Values of the Wilcoxon Rank-Sum
26
1 Introduction
The formulae in this booklet have been arranged by qualification. Students sitting AS Statistics papers should refer to Section 2, pages 2 ? 3. Students sitting A Level Statistics papers should refer to Section 3, pages 4 ? 7.
Pearson Edexcel Level 3 Advanced Subsidiary and Advanced GCE in Statistics
1
Statistical Formulae and Tables ? Issue 1 ? August 2017 ? ? Pearson Education Limited 2017
2 AS Level in Statistics
Population variance, 2, =
x2
N
-
2
=
1 N
(
x
-
)2
Population standard deviation, , =
x2
N - 2 =
1 N
(x
-
)2
Sample variance =
( ) n
1 -
1
x2
-
x
n
2
=
n
1 -
1
(
x
-
x )2
Sample standard deviation =
( ) n
1 -
1
x2
-
x
2
n
=
n
1 -
1(x
-
x )2
Binomial probability calculations:
P(X
=
x) =
n x
px (1 -
)p n - x
Mean = np
Variance = np(1 - p)
For a random sample of nx observations from N(, 2 )
X
-
~
NN((00, ,11) )
n
Test statistic for a binomial proportion using normal distribution:
p^ - p
p(1 - p)
~ NN((00,,11))
n
2
Pearson Edexcel Level 3 Advanced Subsidiary and Advanced GCE in Statistics
Statistical Formulae and Tables ? Issue 1 ? August 2017 ? ? Pearson Education Limited 2017
Product moment correlation coefficient:
r=
S xy
=
(xi - x )( yi - y)
=
{ }{ } Sxx ? Syy
( xi
-
)2
x
( yi
-
)2
y
xi yi
-
(
xi )(
n
)yi
( ) ( )
xi2 -
xi
2
n
yi2 -
yi
2
n
Coefficients for least squares regression line: least squares regression line of y on x is y=a+bx , where a = y - bx
( )( ) the regression coefficient of y on x is b = Sxy = ( ) Sxx
xi - x yi - y xi - x 2
Test for association:
( ) Oi - Ei 2 is approximately distributed as 2
Ei
Pearson Edexcel Level 3 Advanced Subsidiary and Advanced GCE in Statistics
3
Statistical Formulae and Tables ? Issue 1 ? August 2017 ? ? Pearson Education Limited 2017
3 A Level in Statistics
Population variance, 2, =
x2
N
-
2
=
1 N
(
x
-
)2
Population standard deviation, , =
x2
N - 2 =
1 N
(x
-
)2
Sample variance, s2, =
( ) n
1 -
1
x2
-
x
n
2
=
n
1 -
1
(
x
-
x )2
Sample standard deviation, s, =
( ) n
1 -
1
x2
-
x
2
n
=
n
1 -
1(x
-
x )2
Binomial probability calculations:
P(X
=
x) =
n x
px (1 -
)p n - x
Binomial mean = np
Binomial variance = np(1 - p)
For a random sample of nx observations from N(, 2 )
X
-
~
NN((00, ,11))
n
Test statistic for a binomial proportion using normal distribution:
p^ - p
p(1 - p)
~ NN(0(0, ,11))
n
4
Pearson Edexcel Level 3 Advanced Subsidiary and Advanced GCE in Statistics
Statistical Formulae and Tables ? Issue 1 ? August 2017 ? ? Pearson Education Limited 2017
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