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Structured Mathematics
STATISTICS 1
(September 2004 version, based on CC3 & CC4)
Assessment format
Examination
1h 30 mins
Section A: 5 – 7 questions, each worth at most 8 marks.
Section B: 2 questions, each worth about 18 marks.
72 marks.
Topic
Competence
Book Reference
Progress
This section is fundamental to all the Statistics Units (S1-4)
Statistical modelling. 1. Be able to abstract from a
real world situation to a
statistical description (model).
2. Be able to apply an
appropriate analysis to a
statistical model.
3. Be able to interpret and
communicate results. Discuss
their implications in real-world
terms.
4. Appreciate that a model
may need to be progressively
refined
Sampling
5. Understand the meanings of CC3/pp462-473
CC3/8j/
the terms population and CC4/pp421-429
3, 5, 11
sample.
CC4/9a/3
, 5, 7.
6. Be aware of the concept of
random sampling.
MODELLING
DATA PRESENTATION
Classification and
visual presentation
of data.
1. Know how to classify data
as categorical, discrete or
continuous.
2. Understand the meaning of
and be able to construct
frequency
tables
for
ungrouped and grouped data.
Define class intervals and
boundaries.
3. Know how to display
categorical using a pie chart or
a bar chart.
4. Know how to display
discrete data using a vertical
line chart.
5. Know how to display
continuous data using a
histogram for both unequal
and equal class intervals. Use
of term frequency density.
1
CC3 & 4/pp1-3
CC3/pp17-20
CC4/pp17-19
CC3 & 4/p3
CC4/pp24-26
CC3/pp11-17
CC4/pp9-17
CC3/1b/1
&4
CC4/1b/2
-3
Measures of central
tendency and
dispersion.
6. Know how to display and
interpret data on a stem and
leaf diagram.
7. Know how to display and
interpret data on a box and
whisker plot.
8. Know how to display and
interpret
a
cumulative
frequency distribution.
CC3/pp4-11
CC4/pp4-8
CC3/1a/3
CC4/1a/6
CC3/pp117-124
CC4/pp92-99
9. Know how to classify
frequency
distributions
showing skewness. Positive
and negative skewness.
10. Know how to find mean
( x ), median, mode and
midrange.
For raw data,
frequency distributions and
grouped data.
11. Know the usefulness of
each of the above measures of
central tendency.
12. Know how to find range,
percentiles,
quartiles
and
interquartile range.
13. Know how to calculate and
interpret
mean
squared
deviation, root mean squared
deviation, standard deviation
and variance.
14. Be able to use the
statistical functions of a
calculator to find mean, root
mean square deviation and
standard deviation.
15. Know how the mean and
standard
deviation
are
affected by linear coding.
16. Understand the term
outlier.  2SD from the mean
and boxplot criterion.
CC3/pp99-100
CC4/pp20-21,
88,94-95
CC3/2c/9
CC4/1m/
1,10-11
CC3/1m/
3 &1n/3
CC4/1k/3
-4
CC3/2a/4
CC3/pp66-78
CC4/pp58-78
CC3/pp28,30,6266
CC4/pp2, 28-34,
68-78
CC3/1m/
2;1n/5,6,
8;/1d 6(v)
CC4/1d/2
-3;1j/1,2
CC3/pp62-64
CC4/pp68-78
CC3/1n/1
CC4/1j/5;
1k/1, 4
CC4/1f/3,
14-15
CC3/pp34-37
CC4/pp37-44,
447-449
CC3/pp38-42
CC4/pp31-32,
40-42, 449
CC3/1f
CC4/1f/1
CC4/9e/2
CC3/pp47-49
CC4/pp56-57
CC3/1i/2
CC4/1i/1
CC3/p125
CC4/p98 (boxplot
criterion only)
CC4/1m/
3, 10
PROBABILITY
Probability of events
in a finite sample
space.
Probability of two
events which are
1. Know how to calculate CC3/p138
probability of one event.
CC4/p171
CC3/3a/7
CC4/3a/4
2. Understand the concept of a
complementary event and
know that the probability of an
event can be found by finding
that of its complementary
event. P( A)  1  P( A)
3. Know how to draw sample
space diagrams to help
calculate probabilities.
CC3/p139
CC4/p173-4
CC4/3a/6
CC3/p140
CC4/p172-3
CC3/3a/5
CC4/3a/
13-14
2
(i) mutually
exclusive
(ii) not mutually
exclusive
Conditional
probability
4. Know how to calculate the
expected frequency of an
event given its probability.
5. Understand the concepts of
mutually exclusive events and
independent events.
6. Know to add probabilities for
mutually exclusive events.
P( AorB)  P( A)  P( B)
7.
Know
to
multiply
probabilities for independent
events. P( AandB)  P( A) P( B)
8. Know how to use tree
diagrams to assist in the
calculation of probabilities.
9. Know how to calculate
probabilities for 2 events which
are not mutually exclusive.
10 Be able to use Venn
diagrams to help calculations
of probabilities for up to 3
events.
f(A)=nP(A)
CC4/p179, p185
CC4/p179-80
CC4/3b/3
CC4/p185-87
CC4/3c/3
CC3/pp163-9
CC4/pp193-7
CC3/3g/6
CC4/3d/4
CC3/pp142-5
CC4/pp175-6
CC3/3f/2
CC4/3g/
16
CC3/3b/8
CC4/3b/5
CC3/pp137-147
CC4/ pp175-80
P( A  B)  P( A)  P( B)  P( A  B)
11. Know how to calculate the CC3/pp163-174
conditional probabilities by CC4/pp182-191
formula, from tree diagrams or
sample space diagrams.
P( A  B)  P( A) P( B A)
12.Know that P( B A)  P( B) 
B and A are independent.
CC3/3h/2
CC4/3d/B
1-2
CC4/pp185-6
DISCRETE RANDOM VARIABLES
Probability
distributions.
Calculation of
probability,
expectation (mean)
and variance.
Be able to use probability
distribution functions, given
algebraically or in tables.
2. Be able to calculate the
numerical probabilities for a
simple finite distribution.
3. Be able to calculate the
Expectation (mean), E(X), in
simple cases and understand
its meaning.
4. Be able to calculate the
variance, Var(X), in simple
cases.
1.
CC3/p218
CC4/pp233-6
CC3/p224
CC4/p238,
pp253-4
CC3/p231
CC4/pp238-243
CC3/p238
CC3/p240
CC4/p249-50
CC3/4a/1
CC4/4a/
1-2
CC4/4d/2
CC3/4c/5
CC4/4b/3
, 9.
CC3/4d/9
;4e/5
THE BINOMIAL DISTRIBUTION AND HYPOTHESIS TESTING
Situations leading to
a binomial
distribution.
1. Recognise situations which CC3/pp260-3
give rise to a binomial CC4/pp278-283
distribution.
3
CC3/5b/7
CC4/5b/
21
2. Be able to identify the
binomial parameter p, the
probability of success.
Calculations relating 3. Be able to calculate
to binomial
probabilities using the binomial
distribution.
distribution. Including use of
tables of cumulative binomial
probabilities.
4. Know that n C r is the
numbers of ways of selecting r
objects from n.
5. Know that n! is the number
of ways of arranging n objects
in line.
Knowledge of mean. 6. Understand and apply mean
= np.
Calculation of
7. Be able to calculate the
expected
expected frequencies of the
frequencies.
various possible outcomes
from a series of binomial trials.
Hypothesis testing
8. Understand the process of
for a binomial
hypothesis testing and the
probability p.
associated vocabulary.
9. Be able to identify Null and
Alternative Hypotheses ( H 0
and H 1 ) when setting up a
hypothesis test on a binomial
probability model.
10. Be able to conduct
hypothesis tests at various
levels of significance.
11. Be able to identify the
critical
and
acceptance
regions.
12. Be able to draw a correct
conclusion from the results of
a hypothesis test on a binomial
probability.
13. Understand when to apply
1-tail and 2-tail tests.
CC3/pp260-3
CC4/pp278-285
CC3/5a/8
CC4/5b/
13
CC3/5a/8
CC4/5b/4
, 17
CC4/p278
CC4/p278
CC3/pp265-6
CC4/pp286-8
CC3/pp273-5
CC4/pp288-9
CC3/5b/1
CC4/5c/1
CC3/5e/2
CC4/5c/
12
CC3/pp507-10
CC4/pp485-6
CC3/pp539-45
CC4/pp486-9
CC3/10g/
2
CC4/10a/
1-2
CC3/pp539-45
CC4/p489
CC3/10g/
1
CC4/10a/
4
CC4/10a/
7
CC4/pp490-1
CC3/pp539-45
CC4/pp488-491
CC3/pp509-11
CC4/p489
CC3/10g/
2
CC4/10a/
2, 4
CC3/10g/
1
CC4/10a/
1-2
Book references
CC3 Crawshaw and Chambers, A Concise Course in A-level Statistics, 3rd
edition.
CC4 Crawshaw and Chambers, A Concise Course in A-level Statistics, 4th
edition.
[WG: 05/95; PJM 07/95; PEP 10/00, JA 06/04]
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