A LEVEL MATHS - STATISTICS REVISION NOTES
PLANNING AND DATA COLLECTION
PROBLEM SPECIFICATION AND ANALYSIS
What is the purpose of the investigation?
What data is needed?
How will the data be used?
DATA COLLECTION
How will the data be collected?
How will bias be avoided?
What sample size is needed?
PROCESSING AND REPRESENTING
How will the data be ‘cleaned’?
Which measures will be calculated?
How will the data be represented?
INTERPRETING AND DISCUSSING
1 DATA COLLECTION
Types of data Categorial/Qualitative data – descriptive
Numerical/ Quantitative data
Sampling Techniques
Simple random Sampling - each member of the population has an equal chance of being
selected for the sample
Systematic – choosing from a sampling frame - if the data is numbered 1, 2, 3, 4….randomly
select the starting point and then select every nth item in the list
Stratified - A stratified sample is one that ensures that subgroups (strata) of a given population
are each adequately represented within the whole sample population of a research
study.
Sample size from each subgroup 𝑠ize of whole sample × Population of the subgroup
= Size of whole population
Quota Sampling - sample selected based on specific criteria e.g age group
Convenience / opportunity sampling – e.g the first 5 people who enter a Leisure Centre or
teachers in single primary school surveyed to find information about working in
primary education across the UK
Self Selecting Sample – people volunteer to take part in a survey either remotely (internet) or in
person
2 PROCESSING AND REPRESENTATION
Categorial/Qualitative data Pie Charts
Bar charts (with spaces between the bars)
Compound/Multiple Bar charts
Dot charts
Pictograms
1
, Modal Class – used as a summary measure
Numerical/ Quantitative data
Represented using – Frequency diagrams
Histograms
Cumulative Frequency diagrams
Box and Whisker Plots
Measures of central tendency - Mode (can have more than one mode)
- Median – middle value of ordered data
∑ fx
- Mean ∑ or
𝑥 ∑f
n
If the mean is calculated from grouped data it will be an estimated mean
Measures of Spread
- Range (largest – smallest value)
- Inter Quartile Range : Upper Quartile – Lower Quartile (not influenced by extreme values)
- Standard Deviation (includes all the sample )
Finding the quartiles (sample size = n)
n is odd (Data 2, 4, 5, 7, 8, 9, 9)
2 4 5 7 8 9 9
Median
Lower Quartile : middle value Upper Quartile : middle value of data
of data less than the median greater than the median
n is even (Data 2, 4, 5, 5, 7, 8, 9, 10)
2 4 5 5 7 8 9 10
LQ Median UQ
4.5 6 8.5
Lower Quartile : middle value Upper Quartile : middle value
of the lower half of the data of the upper half of the data
2
PLANNING AND DATA COLLECTION
PROBLEM SPECIFICATION AND ANALYSIS
What is the purpose of the investigation?
What data is needed?
How will the data be used?
DATA COLLECTION
How will the data be collected?
How will bias be avoided?
What sample size is needed?
PROCESSING AND REPRESENTING
How will the data be ‘cleaned’?
Which measures will be calculated?
How will the data be represented?
INTERPRETING AND DISCUSSING
1 DATA COLLECTION
Types of data Categorial/Qualitative data – descriptive
Numerical/ Quantitative data
Sampling Techniques
Simple random Sampling - each member of the population has an equal chance of being
selected for the sample
Systematic – choosing from a sampling frame - if the data is numbered 1, 2, 3, 4….randomly
select the starting point and then select every nth item in the list
Stratified - A stratified sample is one that ensures that subgroups (strata) of a given population
are each adequately represented within the whole sample population of a research
study.
Sample size from each subgroup 𝑠ize of whole sample × Population of the subgroup
= Size of whole population
Quota Sampling - sample selected based on specific criteria e.g age group
Convenience / opportunity sampling – e.g the first 5 people who enter a Leisure Centre or
teachers in single primary school surveyed to find information about working in
primary education across the UK
Self Selecting Sample – people volunteer to take part in a survey either remotely (internet) or in
person
2 PROCESSING AND REPRESENTATION
Categorial/Qualitative data Pie Charts
Bar charts (with spaces between the bars)
Compound/Multiple Bar charts
Dot charts
Pictograms
1
, Modal Class – used as a summary measure
Numerical/ Quantitative data
Represented using – Frequency diagrams
Histograms
Cumulative Frequency diagrams
Box and Whisker Plots
Measures of central tendency - Mode (can have more than one mode)
- Median – middle value of ordered data
∑ fx
- Mean ∑ or
𝑥 ∑f
n
If the mean is calculated from grouped data it will be an estimated mean
Measures of Spread
- Range (largest – smallest value)
- Inter Quartile Range : Upper Quartile – Lower Quartile (not influenced by extreme values)
- Standard Deviation (includes all the sample )
Finding the quartiles (sample size = n)
n is odd (Data 2, 4, 5, 7, 8, 9, 9)
2 4 5 7 8 9 9
Median
Lower Quartile : middle value Upper Quartile : middle value of data
of data less than the median greater than the median
n is even (Data 2, 4, 5, 5, 7, 8, 9, 10)
2 4 5 5 7 8 9 10
LQ Median UQ
4.5 6 8.5
Lower Quartile : middle value Upper Quartile : middle value
of the lower half of the data of the upper half of the data
2
