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D1 Planning and collecting data
KS3 Mathematics
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D1
D1
D1
D1
D1.1 Planning a statistical enquiry
Contents
D1 Planning and collecting data
D1.2 Collecting data
D1.3 Organizing data
D1.4 Writing a statistical report
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Specifying the problem
The first step in planning a statistical enquiry is to decide what problem you want to explore.
This can be done by asking questions that you want your data to answer and by stating a hypothesis.
For example, suppose we wish to investigate the lengths of words used in newspapers.
We could ask:
“Do different types of newspaper use different length words?”
A hypothesis is a statement of something that you believe to be true but do not have any evidence to support.
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Specifying the problem
Related questions could include:
“Is there a link between the lengths of the words used and the lengths of the sentences for a particular newspaper?”
“Is there a difference between the use of two- and three-letter words?”
A possible hypothesis could be:
“Tabloid newspapers use shorter words to appeal to a wider audience.”
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Deciding on the data
The next step is to decide what data is needed and where it can be collected from.
Data can be collected from a primary source or a secondary source.
Data can be collected from a primary source or a secondary source.
Data from a primary source is data that you have collected yourself, for example:
Data from a secondary source is data that you have collected from somewhere else including the Internet, reference books or newspapers.
From a survey or questionnaire of a group of people.
From an experiment involving observation, counting or measuring.
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Sources of data
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Choosing the sample
When collecting data it is usually impractical to include every member of the group that is being investigated.
How big should a sample be?
The sample should be as large as possible.
This will depend on the time and resources available.
If the sample size is too small, then the results will be unrepresentative.
A sample is therefore choose to represent the group.
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Choosing the sample
It is important that the sample is representative of the group that is being investigated.
Suppose, for example, that you wish to investigate the favourite sports of 11 to 15 year-olds.
Would it be reasonable to question a sample of people outside a football ground following a game?
Can you suggest a better sample?
You would have to make sure that you ask equal numbers of girls and boys and that the sample is spread out across all age groups in the range.
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Choosing units
If your statistical investigation involves measurement then you must decide what units to use and to what degree of accuracy.
Suppose, for example, that you wish to investigate the relationship between age and height.
How will you measure age?
How will you measure height?
In weeks? In months?
In years and months? In years?
In metres?
In inches? In centimetres?
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Planning a statistical enquiry
Once you have decided on:
you can start the next stage which is to design a data collection sheet or questionnaire.
the purpose of the enquiry,
the type of data that will be collected and where it will come from,
and the sample size and type,
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D1
D1
D1
D1
D1.1 Planning a statistical enquiry
D1.2 Collecting data
Contents
D1.3 Organizing data
D1 Planning and collecting data
D1.4 Writing a statistical report
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Collecting data
Data can be collected using a questionnaire or a data collection sheet.
A questionnaire is used when you wish to ask a sample of people a series of structured questions
relevant to your line of enquiry.
A questionnaire is used when you wish to ask a sample of people a series of structured questions
relevant to your line of enquiry.
A data collection sheet or observation sheet is used when recording results involving counting, measuring or observing. It can also be used to collect the answers to a few simple questions.
A data collection sheet or observation sheet is used when recording results involving counting, measuring or observing. It can also be used to collect the answers to a few simple questions.
Data can also be collected from secondary sources such as the Internet, newspapers or reference books.
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Designing a questionnaire
When designing you own questionnaire you should try to follow these rules:
1) Provide an introduction, so that the person filling in the questionnaire knows the purpose of your enquiry.
2) Write questions in a sensible order, putting easier questions first.
It is important to design a questionnaire so that:
People will co-operate and answer the questions honestly.
The answers to the questions can be analysed and presented.
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Designing a questionnaire
3) Make sure that questions are not embarrassing or personal.
For example, you need to think carefully about questions asking about age or income.
Do not ask : How old are you?
A better question is : Tick one box for your age group.
15-20 21-25 26-30 31 +
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Designing a questionnaire
People could answer :
Yes
No
Not much
Only the best bits
Once a day
Sometimes
4) If possible, write questions so that they have a specific answer.
Did you see the Olympics on TV?
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Designing a questionnaire
A better question would be:
How much of the Olympics coverage did you watch?Tick one box only.
None
Less than 1 hour a day
Between 1 to 2 hours a day
More than 2 hours a day
Every eventuality has been accounted for and the person answering the question cannot give another choice.
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How would you rate the leisure facilities available in your local area? Tick one box only.
Designing a questionnaire
A scale can be used when asking for an opinion.
Excellent UnsatisfactoryPoorSatisfactoryGood
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Designing a questionnaire
5) Do not ask leading questions.
The question below conveys a particular opinion:
A better question is :
Which one of the following sports do you like the best?
football rugby tennis golf cricket boxing
Don’t you agree that football is the best sport?
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Suggest a better question
How much do you weigh?
This is too personal, also some people don’t know their weight.
Underweight Average weight Overweight
Would you consider yourself to be:
A better question would be:
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Suggest a better question
Most people use a deodorant, do you ?
Which make of deodorant do you use ?
Male:
Female: Sure Impulse Dove Other None
Lynx OtherAdidas Slazenger None
Please circle any that apply.
This is a leading question and may offend people.
A more useful question would be:
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Suggest a better question
The intervals given overlap. Also, if a person has read more than 6 books there is nowhere to tick.
A better question would be:
How many books did you read last month?Tick one box.
0-2 3-5 6-8 8+
How many books did you read last month?
0-2 2-4 4-6
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Trialling a questionnaire
Once you have written a questionnaire it is a good idea to try it out on a small sample of people. This is called a pilot survey.Note down their responses and use these to refine any questions that are causing difficulty.
Do I use a tick or a cross to show the
box I want?
What does this question mean?
I don’t want to answer this question because
it’s too personal.
There isn’t a box to cover my answer.
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Designing a data collection sheet
A data collection sheet can be used to record data that comes from counting, observing or measuring.
It can also be used to record responses to specific questions.
To investigate a claim that the amount of TV watched has an impact on weight we can use the following:
age gender height (cm) weight (kg) hours of TV watched per week
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Using a tally chart
When collecting data that involves counting something we often use a tally chart.
The below tally chart can be used to record people’s favourite snacks.
favourite snack tally frequency
crisps
fruit
nuts
sweets
The tally marks are recorded, as responses are collected,and the frequencies are then filled in.
13
6
3
8
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Using a tally chart
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D1
D1
D1
D1
D1.3 Organizing data
Contents
D1.2 Collecting data
D1 Planning and collecting data
D1.1 Planning a statistical enquiry
D1.4 Writing a statistical report
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Categorical data
Categorical data is data that is non-numerical. Categorical data is data that is non-numerical.
For example:
Sometimes categorical data can contain numbers.
For example:
favourite football team
eye colour
birth place.
favourite number
last digit in your telephone number
most used bus route.
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Discrete and continuous data
Discrete data can only take certain values. Discrete data can only take certain values.
Continuous data comes from measuring and can take any value within a given range.
Continuous data comes from measuring and can take any value within a given range.
Numerical data can be discrete or continuous.
For example:
For example:
shoe sizes the number of children in a class the number of sweets in a packet.
the weight of a banana the time it takes for pupils to get to school the height of 13 year-olds.
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Discrete or continuous data
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Using a frequency table
Once data has been collected it is often organized into a frequency table.
This frequency table shows the favourite take-away meals of a group of pupils:
Favourite take-away
Pizza
Fish and chips
Burgers
Indian
Frequency
11
7
8
5
Chinese 8
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Grouping discrete data
A group of 20 people were asked how much change they were carrying in their wallets. These were their responses:
34p£1.7283p £6.36
£4.07£2.97£3.53 6p
£9.5434p£1.68 50p
82p£7.54£1.09 £2.81
£2.4346p£1.70 £1.29
Each amount of money is different and the values cover a large range.
This type of data is usually grouped into equal class intervals.
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Choosing appropriate class intervals
When choosing class intervals it is important that they include every value without overlapping and are of equal size.
For the following data:
34p£1.7283p £6.36
£4.07£2.97£3.53 6p
£9.5434p£1.68 50p
82p£7.54£1.09 £2.81
£2.4346p£1.70 £1.29
We can use class sizes of £1:
£0.01 - £1.00, £1.01 - £2.00, £2.01 - £3.00, £3.01 - £4.00,
£4.01 - £5.00, Over £5. This is an open class interval.
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Over 5.00
4.01 - 5.00
3.01 - 4.00
2.01 - 3.00
1.01 - 2.00
0.01 - 1.00
FrequencyAmount of money (£)
3
1
1
3
5
7
Choosing appropriate class intervals
34p£1.7283p £6.36
£4.07£2.97£3.53 6p
£9.5434p£1.68 50p
82p£7.54£1.09 £2.81
£2.4346p£1.70 £1.29
Complete the following frequency table for this data:
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Choosing appropriate class intervals
The size of the class intervals depends on the range of the data and the number of intervals required.
Explain why class sizes of £5 would be inappropriate.
Could we use a class size of 20p?
For the following data:
34p£1.7283p £6.36
£4.07£2.97£3.53 6p
£9.5434p£1.68 50p
82p£7.54£1.09 £2.81
£2.4346p£1.70 £1.29
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Grouping continuous data
Continuous data is usually grouped into equal class intervals.
What is wrong with the class intervals in this grouped frequency table showing lengths?
30 ≤ length
20 ≤ length ≤ 30
10 ≤ length ≤ 20
0 ≤ length ≤ 10
FrequencyLength (cm)
This is an open class interval.
30 ≤ length
20 ≤ length < 30
10 ≤ length < 20
0 ≤ length < 10
FrequencyLength (cm)
The class intervals are written using the symbols ≤ and <.
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Grouping continuous data
Continuous data is usually grouped into equal class intervals.
What is wrong with the class intervals in this grouped frequency table showing weights?
Weight (g) Frequency
0 < weight < 10
10 < weight < 20
20 < weight < 30
30 < weight
Weight (g) Frequency
0 ≤ weight < 10
10 ≤ weight < 20
20 ≤ weight < 30
30 ≤ weight
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Using two-way tables
A two-way table can be used to organize two sets of data.
For example, pupils from Years 7, 8 and 9 were asked what they usually did during their lunch break. This two-way table shows the results:
Year 7
Year 8
Year 9
Eat school dinners
35
29
38
Eat a packed lunch
42
34
32
Eat at home
19
22
18
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D1
D1
D1
D1
D1.4 Writing a statistical report
Contents
D1.3 Organizing data
D1.2 Collecting data
D1 Planning and collecting data
D1.1 Planning a statistical enquiry
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The data collection cycle
The following diagram shows the stages needed to conduct a statistical enquiry.
Specify the problem and plan
Process and display the data
Collect the data from a variety of
sources
Interpret and discuss the
results
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The data collection cycle
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Writing a statistical report
Once you have planned, collected and processed data relevant to a statistical enquiry you will often have to communicate your findings in the form of a report.
A report should contain the following:
A description of what sources were used including a justification of the type and size of any samples used.
An introduction stating the purpose of the survey and any initial conjectures which you plan to investigate.
Calculations, such as the mean, median and mode, to give an overall picture of the data.
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Writing a statistical report
Sometimes your data will give results that you did not expect. These will lead to new lines of enquiry which you should investigate if possible.
Problems or ambiguities that arose during the course of the investigation and how you dealt with them.
A summary of the conclusions shown by the data, not forgetting to refer back to your initial hypothesis.
Tables or graphs of the results, using ICT as appropriate. (Remember to justify you choice of what is presented).
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Writing a statistical report
Collect the relevant data and write a statistical report investigating one of the following:
The types of sports young people take part in outside of school hours.
How pupils travel to school.
The difference in word lengths used in men’s and woman’s magazines.
Use of mobile phones among teenagers.
The relationship between hand span and foot length.
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