1. GCSE Statistics Support Event
Wednesday 23/05/2108
Corr’s Corner Hotel
9.30 to 15.30

2. Education Manager: Michael McEnery
ext 2170
Subject Support Officer: Nuala Tierney
Chair of Examiners: Ruth Crooks
Chief Examiner: Darren Owens
Principal Examiners: James McAuley, Conor Sweeney, Brenda Crossen

4. Proposed Amendments to Specification
use simple cases of hypothesis testing using H0 and H1 notation, including knowledge of one- and two-tailed tests; page 14 of specification
These amendments are with CCEA Regulator and awaiting decision. Microsite will inform you of decision before September 2018.
use simple cases of hypothesis testing using Ho and H1 notation, including knowledge of one- and two-tailed tests; and
This has been removed as the level of complexity of this topic is too advanced for this course and is not in keeping with the spirit of this specification. This is not included in the comparable specifications for AQA and Edexcel. The DfE guidance on this topic suggests that it should be covered at A2.
The binomial distribution as a model
demonstrate understanding of the binomial distribution as a commonly used model for experiments;
This has been included to replace hypothesis testing to provide an example of a probability distribution for a discrete random variable to complement the Normal distribution which is already included.
use binomial expansions to calculate probabilities;
As above.

5. Access to Resources – C2k Fronter Room
Send details to

6. Session 1
The Statistical Problem Solving Process

7. The timeline can be accessed from the following link: http://www

9. The RSS rebranded in 2014 when the current logo and strapline was developed.
The reason for changing is that we wished to have a brand that spoke to the important role that statistics and data play in everyone’s lives, and an identity that reflected what the Society is today: professional, modern and inclusive.

10. The 1857 RSS logo

11. The RSS logo
One of the original aims of the Society was to present statistical facts for others to interpret hence the original badge of the wheatsheaf with the latin motto "aliis exterendum" which translates as "to be threshed by others". This purist approach of presenting statistics without interpretation was soon found to be untenable and the motto was dropped in 1857 when the wheatsheaf was also tidied up.
The First 100 Years: I.D. Hill JRSS Series A (General), Vol. 147, No. 2 (1984), p.133
Explanation from the archivist for RSS, The Royal Statistical Society

12. Statistical problem solving
Posing a question
Planning
Collecting data
Processing representing and Analysing data
Discussing and Interpreting results
Communicating in a variety of forms
Evaluating

13. the statistical problem solving process.
GCSE Statistics
Understand and use
the statistical problem solving process.
Appreciate the use of Statistics in real life
Synoptic – seeing things together …

14. The statistical problem solving process
Real world Statistical world

15. The statistical problem solving process
Statistical world

16. The statistical problem solving process
Real world

17. The statistical problem solving process
Real world and Statistical modelling

18. Subject-specific skills
Content skills
and
Process skills
Statistical techniques
Statistical thinking

19. Subject-specific skills
Using and applying
standard statistical techniques
Interpreting and reasoning statistically
Addressing statistical problems by
using the statistical enquiry cycle

20. Using and applying standard statistical techniques
Collecting and representing data
Calculating summary statistics and calculating probabilities
Accurately recalling appropriate facts, terminology, definitions and procedures
Using and interpreting appropriate notation correctly

21. Interpreting and reasoning statistically
Interpreting statistical information and results in the context of the given problem
Reasoning statistically to draw conclusions from statistical information
Communicating findings accurately
Making deductions and inferences

22. Addressing statistical problems using the statistical enquiry cycle
Assessing the appropriateness of statistical methodologies
Assessing the appropriateness of the conclusions drawn
Translating a real world problem into a series of statistical processes
Critically evaluating a given way of presenting information
Evaluating methods used and results obtained in the context of the given problem
Evaluating solutions to identify how they may have been affected by assumptions made.

23. Assessment Objectives
Demonstrate knowledge and understanding, using appropriate terminology and notation, of standard techniques used to
Collect and represent data
Calculate summary statistics and probabilities
Interpret statistical information and results in context and reason statistically to draw conclusions
Assess the appropriateness of statistical methodologies and the conclusions drawn through the application of the statistical enquiry cycle.

24. Becoming confident with Statistics
Subject-specific skills
Content skills
and Process skills
Statistical techniques
and Statistical thinking

25. Becoming confident with Statistics
Every Statistics lesson is an opportunity to develop Statistical Techniques
Every Statistics lesson is an opportunity to develop Statistical Thinking
Statistical problem solving process
Statistics in real-life

26. Statistics in real-life
The timeline can be accessed from the following link:

27. Timeline of Statistics

28. Specification Guidance
Session 2
Specification Guidance

29. Statistical Enquiry Cycle
Planning
Data collection
Processing, representing and analysing data
Discussing and interpreting
Communicating and evaluating
Statistical Enquiry Cycle

30. Assessment Objectives
AO1
demonstrate knowledge and understanding, using appropriate terminology and notation, of standard statistical techniques used to:
collect and represent data; and
calculate summary statistics and probabilities;
55%
AO2
interpret statistical information and results in context and reason statistically to draw conclusions;
25%
AO3
assess the appropriateness of statistical methodologies and the conclusions drawn through the application of the statistical enquiry cycle.
20%

31. AO Weightings

32.  AO Example: Pictogram KEY: Monday Tuesday Wednesday Thursday Friday
The pictogram shows the number of pupils absent each day during one week.
KEY: 
= 2 pupils
Monday
Tuesday
Wednesday
Thursday
Friday

33. Brief Outline of Content
Planning and data collection
Data organisation
Diagrams
Calculations
Probability
Special distributions

34. Planning and Data Collection
Questions and hypotheses
Variables, data and data sources
Sampling
Obtaining data: experiment, survey, etc
Problems: outliers, non-response, etc

35. Questions and Hypotheses
HYPOTHESIS
Does more revision result in a better mark?
There is a positive correlation between the number of hours spent on revision and the mark in the test.
Is the weather better at the coast than inland?
The average number of hours of sunshine is greater at the coast than inland.
Is GCSE Statistics worth doing?
Those who have GCSE Statistics get better A-Level results than those who don’t.

36. Simple Random Sample

37. Simple Random Sample

38. Simple Random Sample

39. Simple Random Sample

40. Simple Random Sample

41. Systematic Sample

42. Systematic Sample

43. Systematic Sample

44. Systematic Sample

45. Stratified Sampling
Sample
Population

46. Cluster Sampling
Theoretical
structure of the
Population

47. Cluster Sampling
Actual
structure of the
Population

48. Select one cluster as the sample
Cluster Sampling
Select one cluster as the sample

49. Data Organisation Tally chart Frequency table Grouped frequency table
Two-way table
Venn diagram
Stem and leaf diagram

50. Venn Diagram
Even
Prime 5 4 2 3 6 1

51. Venn Diagram
Even
Cube 4 6 8 27 1
Square 64 9

52. Diagrams Pictogram Cumulative frequency Bar chart Box plot
Compound bar chart
Multiple bar chart
Pie chart
Comparative pie chart
Histogram
Cumulative frequency
Box plot
Scatter diagram
Time series
Control chart
Population pyramid
Choropleth map

53. Bar Charts Compound (stacked) Multiple (grouped) X Y Z A B C Frequencyor
Percentage
A B C

54. Comparative Pie Chart r R
𝑓 𝑟 2 = 𝐹 𝑅 2

55. Histogram
Frequency
On Foundation Tier, the class widths will be equal so knowledge of frequency density is not required.
Length (cm)

56. Histogram
Frequency
Density
On Higher Tier, the class widths may be unequal so frequency density is required.
Length (cm)

57. Cumulative Frequency

58. Box Plot
Smallest
Value
Largest
Median LQ UQ
25%
50%
50%

59. Scatter Graphs ( 𝒙 , 𝒚 ) A line of best fit should
Response
Variable
Explanatory y
( 𝒙 , 𝒚 )
A line of best fit should
start and end at the
first and last points. x

60. Time Series
Sales (£000)

61. Control Chart 1 2 3 4 5 6 7 8 Sample Number Upper action Line
Upper warning line
Lower action Line
Lower warning line
Target line
Sample Number

62. Control Chart Process is under control 1 2 3 4 5 6 7 8 Sample Number
Upper action Line
Upper warning line
Lower action Line
Lower warning line
Target line
Sample Number
Process is under control

63. Control Chart 1 2 3 4 5 6 7 8 Sample Number Upper action Line
Upper warning line
Lower action Line
Lower warning line
Target line
Sample Number

64. Control Chart Process needs checked Process needs checked
Upper action Line
Upper warning line
Lower action Line
Lower warning line
Target line
Sample Number
Process needs checked
Process needs checked

65. Control Chart 1 2 3 4 5 6 7 8 Sample Number Upper action Line
Upper warning line
Lower action Line
Lower warning line
Target line
Sample Number

66. Control Chart Process is out of control Process is out of control
Upper action Line
Upper warning line
Lower action Line
Lower warning line
Target line
Sample Number
Process is out of control
Process is out of control

67. Control Chart 1 2 3 4 5 6 7 8 Sample Number Upper action Line
Upper warning line
Lower action Line
Lower warning line
Target line
Sample Number

68. Assumption Grammar School
Population Pyramid
80 +
70 – 80
60 – 70
50 – 60
30 – 40
20 – 30
40 – 50
10 – 20
0 – 10
MALE
FEMALE
GCSE Statistics

69. Assumption Grammar School
Choropleth Map
GCSE Statistics

70. Assumption Grammar School
Choropleth Map
GCSE Statistics

71. Calculations Mean, mode, median, range, geometric mean
Median, quartiles, IQR
Deciles and percentiles
Moving averages
Standard deviation
Index numbers: simple, chain base, weighted
Standardised scores
Product moment
Spearman’s rank

72. Percentiles 17
P34

73. Any correct formula/method may be used.
Standard Deviation
Any correct formula/method may be used.
𝜎= 𝑓𝑥 𝑓 − 𝑓𝑥 𝑓 2
Candidates can use calculator functions to calculate  but should know which button(s) to use.
Knowledge of s2 as an estimate for  2 is not needed and should not be used.
𝜎= (𝑥− 𝑥 ) 2 ) 𝑛

74. Simple Index Numbers
Year
2012
2014
2015
2016
2017
Price
38p
39p
44p
48p
47p
51p
Simple Index No.
100
102.6
115.8
126.3
123.7
134.2
Index number n years after the base year = 𝑃 𝑛 𝑃 0 ×100
Index number after 4 years = ×100
= 123.7
Price has increased by 23.7% since 2012.

75. Chain Base Index Numbers
Year
2012
2014
2015
2016
2017
Price
38p
39p
44p
48p
47p
51p
Chain base index No.
100
102.6
115.8
126.3
123.7
134.2
Chain base index number = 𝑃 𝑛 𝑃 𝑛−1 ×100
Chain base index number for 2016 = ×100
= 97.9
Price has decreased by 2.1% since 2015

76. Probability The probability scale Relative frequency as an estimate
Equally likely outcomes
Expected frequency
Risk
Venn diagrams
Tree diagrams

77. Absolute Risk

78. Distributions The binomial distribution as a model
The normal distribution as a model

79. Guidance on Unit 2 (pre-release)
Session 3
Guidance on Unit 2
(pre-release)

80. Unit 2
Unit 2 is designed to give candidates the opportunity to apply their knowledge of the Statistical Enquiry Cycle to published statistics in a prescribed context.
This is a unique feature of the CCEA GCSE Statistics.

81. Unit 2
The Unit 2 examination will test candidates’ knowledge and understanding of the components of the Statistical Enquiry Cycle as applied to the prescribed context.
Contexts will be realistic, current and local.
Pre-release material will be uploaded to the GCSE Statistics microsite in September for the forthcoming examination.
Candidates will not need to memorise any information from the pre-release material and will not need a copy of it in the examination.

82. Unit 2 directly related to pre-release;
Unit 2 is not an investigation, nor will the entire paper be based on the pre-release material.
Questions will fall into one of three categories:
directly related to pre-release;
inspired by or indirectly related to pre-release;
not connected to pre-release.

83. Example

84. Foundation Tier New Topics
Session 4
Foundation Tier New Topics

85. Foundation Tier ‘New’ Topics
Correlation and Correlation coefficients
Data sets
Sampling
Control Charts
Simple index numbers

86. Statistics in the news
Franz H. Messerli, M.D.

87. The Vending Machine

88. Correlation and Correlation Coefficients
The Vending Machine
Chocolate Bar
Weight (g)
Energy (kcal)
Manufacturer
Price
Option 40 48
245
Manufacturer 1
£0.80
Option 42 51
228
Option 44 50
248
Option 45 40
203
Manufacturer 2
Option 46 46
Option 47 55
186
Manufacturer 3
£2.00
Option 50
236
Option 51 38
198
Option 52 43
204
Manufacturer 4
Option 53 36
194
Option 54 42
229
Option 55 54
278
£0.95
Option 56 45
240
Option 57
Option 60
199
£0.90
Option 63 49
249

89. Correlation and correlation coefficients

90. Correlation and Correlation coefficients

91. Correlation and Correlation coefficients

92. Correlation and Correlation coefficients
Weight (g)
Energy (kcal) 48
245 51
228 50
248 40
203 46 55
186
236 38
198 43
204 36
194 42
229 54
278 45
240
199 49
249 r=
Weight (g)
Energy (kcal) 48
245 51
228 50
248 40
203 46
236 38
198 43
204 36
194 42
229 54
278 45
240
199 49
249 r=

93. Data sets The Vending Machine Chocolate bars
The Melmount Medical Centre
Quality Irish Potatoes
Crisps (Multipacks)
Food Hampers

94. Sampling

95. Control Charts
The graph below shows values within the action lines. No action is required. It is not possible for every sample mean to be exactly on target.

96. Control Charts
The graph below shows the quality assurance chart for a soft drink company. They measure a sample of cans every half hour and record the sample median on the chart. The target median is set at 332ml to ensure the capacity doesn’t drop below the stated amount (330ml).

97. Simple index numbers
For example, for the data in the table below, calculate the simple price indices for 2015 and 2016 relative to 2014 (the base period)
These index numbers show that:
prices in 2015 increased by 5% relative to 2014
prices in 2016 increased by 8.9% relative to 2014

98. New Topics for Higher Tier
Session 5
New Topics for
Higher Tier

99. ‘New’ Topics Cumulative frequency diagrams (discrete data)
Use of the geometric mean
Correlation and regression
Absolute and relative risk
The binomial distribution

100. Cross-curricular Themes Thinking skills and Personal Capabilities
Session 6
Cross-curricular Themes
Thinking skills and Personal Capabilities

101. Cross-Curricular Skills
Communication skills
Using Mathematics skills
Using ICT skills
Thinking Skills and Personal Capabilities
Self-Management skills
Working with Others Skills
Problem Solving skills

102. The statistical problem solving process
Students should be able to understand and use the statistical problem-solving process by:
planning;
collecting data;
processing, representing and analysing data;
discussing and interpreting results; and
communicating in a variety of forms such as written, tabular or diagrammatic.

103. Communication Skills
Written Communication Skills
Reading
Writing
Oral Communication Skills
Listening
Presenting

104. Not just literacy but Statistical literacy
True ease in writing comes from art, not chance,
as those move easiest who have learn’d to dance.
Alexander Pope 1688 – 1744
The limits of my language mean the limits of my world.
Ludwig Wittgenstein 1889 – 1951

105. Using Mathematics
Understand and use positive and negative numbers of any size in practical contexts.
Carry out statistical calculations with numbers of any size in practical contexts, to a suitable degree of accuracy.

106. Using Mathematics
Understand and use equivalences between fractions, decimals and percentages.
Understand, use and calculate ratio and proportion, including problems using scale.

107. Understand and use statistical formulae.
Using Mathematics
Understand and use statistical formulae.
Calculating the angle for a sector in a pie chart.
Frequency density for a histogram
Calculation of arithmetic mean
Range
Interquartile range
Probability
4 point moving averages

108. Using ICT
Scientific calculators
Spreadsheets
The Internet

109. Use techniques such as names drawn from a hat, dice, cards, random number lists or random numbers from a calculator or spreadsheet to select a random sample.
Collect data using methods such as experiment, data logging, survey, reference, census, simulation, questionnaires and/or observation and demonstrate understanding of when these methods are appropriate.
Calculate a product moment correlation coefficient using calculator functions or spreadsheet functions and demonstrate knowledge that correlation coefficients are used when the data are random on random.
Calculate standard deviation using a formula or calculator functions for a small set of ungrouped data or large set of grouped data and interpret standard deviation as a measure of spread.
Use and interpret a given line of best fit for a scatter diagram including outputs from software.

110. Working with others Self-management Interpersonal skills
Working in a team
Leading others
Self-management
Aiming High
Remaining positive

111. Problem Solving skills
Statistical problem solving
Creativity
Problem Solving
Ask Questions
Why? Who? What? Where? When? How? Which?

112. Problem solving skills
A data rich world - Knowledge Economy
Human Endeavour – ‘Curiosity based research’
Beyond the Timeline …?