Transcript Statistics Coursework Guidelines

Girls are better
at maths than
boys
Statistical
Coursework
There are more
vowels used in a
page written out in
French rather than
English.
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Assessing the task
Statistical coursework is marked under three headings:
• Specifying the problem and planning
• Collecting, processing and representing the data
• Interpreting and discussing the results
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1. Specifying the problem and planning
This strand is about choosing a problem and deciding what
needs to be done, then doing it. The strand requires you to
provide clear aims, consider the collection of data, identify
practical problems and explain how you might overcome
them.
For the higher marks you need to decide upon a suitable
sampling method, explain what steps were taken to avoid
possible bias and provide a well structured report.
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2. Collecting, processing and representing
the data
This strand is about collecting data and using the most
appropriate statistical techniques and calculations to
process and represent the data. Diagrams should be
appropriate and calculations mostly correct.
For the higher marks you will need to accurately use
higher level statistical techniques and calculations from the
higher tier GCSE syllabus content.
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3. Interpreting and discussing the results
This strand is about commenting, summarising and
interpreting your data. Your discussion should link back to
the original problem and provide an evaluation of the work
undertaken.
For the higher marks you will need to provide sophisticated
and rigorous interpretations of your data and provide an
analysis of how significant your findings are.
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Getting started – setting up your hypothesis
Moderator comment:
Your statistical task must always start with a ‘hypothesis’ where
you state exactly what you are investigating and what you expect
to find.
It does not matter whether your hypotheses are true or false –
you will still gain marks if your hypothesis turns out to be false.
Your hypothesis should be clearly stated and testable.
 Brainstorm possible hypotheses for a task relating to the
differences and similarities between boys and girls.
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Choosing the right sample
Once you have decided your aims and set up a hypothesis then it is
important to consider how you will test your hypothesis.
To this end, there should be a discussion of what data is needed to
test the hypothesis, how much and what type.
Your sample
size must
be at least
30
Suggest the data that would be relevant to testing the
following hypothesis:
“In any particular age group, boys are taller than girls”
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Sampling techniques include:
Random sampling is where each member of the population has
an equally likely chance of being selected. An easy way to do this
would be to give each person a number and then choose the
numbers randomly.
Systematic sampling is the similar to random sampling except
that there is some system involved such as numbering each
person and then choosing every 20th number to form the sample.
Stratified sampling is where each person is placed into some
particular group or category (stratum) and the sample size is
proportional to the size of the group or category in the population
as a whole.
Convenience sampling or opportunity sampling is one which
involves simply choosing the first person to come along …
although this method is not particularly random!
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Imagine you are going to conduct a survey of the opinions of
pupils at this school about school uniform.
Describe how you would collect the following samples:
a random sample
a systematic sample
a stratified sample
a convenience sample
You must be very careful to avoid any possibility of bias in your
work. For example, in making comparisons it is important to ensure
that you are comparing like with like. For example, a comparison
between the number of graphics used in a newspaper and the
number in a magazine must include some consideration of the
relative sizes of the two publications – newspapers are larger than
magazines.
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Using
the table: and calculations
Methods
• What do you notice about the average of the length and weight?
•You
What
cando
represent
you notice
theabout
data using
the spread
statistical
of the
calculations
length andsuch
weight?
as the
•mean,
Doesmedian,
the information
mode, range
support
andthe
standard
hypothesis?
deviation.
E.g. Hypothesis being tested:
“Students are better at estimating the length of a line
than the weight of a package”.
Tabulated calculations:
Length(cm)
Mean
15.9
Median
15.5
Mode
14
Range
8.6
St Dev
1.2
Weight (g)
105.2
100
100
28
2.1
It is important to consider
whether information on all
of these statistical
calculations is essential.
Note: the actual length of the line is 15cm and the weight of the
package is 100g.
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Points to note about the statistical calculations:
• The mean, mode and median are all measures of central tendency
• The range, inter-quartile range, (percentiles) and standard
deviation are all measures of spread (variability).
• When comparing two distributions you should consider an average
and a measure of spread.
• Choose the best representative value for you data (e.g. the
median). Do not be repetitive. Ensure a good range of appropriate
techniques, including some higher tier techniques if appropriate.
• GCSE Stats students should try to include calculations such as
standard deviation (measure of spread) and Spearman’s Rank
Correlation (measures the strength of correlation between two
variables).
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Graphical representation
It may be useful to show your results using graphs and diagrams
as sometimes it is easier to see trends.
Graphical representation might include:
Pie charts, bar charts, scatter diagrams, stem and leaf diagrams,
histograms, cumulative frequency graphs and box-whisker
diagrams.
Moderator comment:
You should only use appropriate diagrams and graphs.
Remember: you should comment on why you are choosing to
include a particular diagram and, after you have drawn it, what
inferences you can make based on the diagram.
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Matching the graph to the purpose of the investigation
The four main reasons for collecting data are:
• Describing
• Comparing
• Summarising
• Generalising
Here are a few examples to give you an idea of what is meant above.
Purpose
Typical statements
Describing
There are 14 boys and 15 girls
The tallest person in the class is a girl
Summarising
The modal class height is 1.50-1.55m
The heights of Paul and Tom are typical of the class
Comparing
There are more boys than girls
There are more tall girls than tall boys
Generalising
Girls seem to be taller than boys at this age
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This table shows you which diagrams and calculations fit each
purpose:
Types of
data
Purposes
Describing Summarising
Comparing
Categories
Bar chart
Pie chart
Bar charts
Pie charts
Discrete
variable
Bar chart
Pie chart
Stem plot
Mean, mode
Median
Range
Bar charts
Pie charts
B-B stem
plots
Continuous Stem plot
variable
Histogram
Mean, mode
Median
Range
B-B stem
plots
Histograms
Bivariate
Line of fit
Scatterplot
(discrete or
continuous)
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Generalsising
Line of fit
Summarising and interpreting the data
You should refer to your original hypothesis when you summarise
your results.
Moderator comment:
In your conclusion you should also suggest limitations to your
investigation and explain how these might be overcome.
You may wish to discuss:
• sample size
• sampling methods
• biased data
• other difficulties
Hint:
You need to appreciate that the
data is more secure if the sample
size is 500 rather than 50.
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Extending the task
To gain better marks in your coursework you should extend the
task in light of your findings.
In your extension you should:
• Give a clear hypothesis
• Collect further data if necessary
• Present your findings using charts and diagrams as
appropriate
• Summarise your findings referring to your hypothesis
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Using a computer
It is quite acceptable that calculations and representations are
generated by computer, as long as any such work is accompanied
by some analysis and interpretation.
Accuracy check
Whether you have computer-generated or hand-drawn tables
and diagrams you should check the following:
• The tables are clear
• The diagrams are labelled clearly
The diagrams have titles
There is a wide variety of diagrams
They are all appropriate
Remember there is no need to use every type
• The calculations are clearly written out
They are appropriate and relevant
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In this presentation I have tried to give you some hints on
approaching statistical coursework to gain the best possible mark.
This list of statistics is often useful in investigative tasks:
•
•
•
•
•
•
•
•
•
•
Calculating averages (mean, mode and median)
Finding the range
Pie charts, bar charts, stem and leaf diagrams
Constructing a cumulative frequency graphs
Finding the inter-quartile range
Histograms
Calculating the standard deviation
Drawing a scatter graph and line of best fit
Sampling techniques
Discussing bias
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Remember:
None of these
will gain you
marks if they
are not
appropriate
and relevant to
your enquiry!