© Boardworks Ltd 2004 1 of 43 D1 Planning and collecting data KS3 Mathematics.

© Boardworks Ltd 20041 of 43

D1 Planning and collecting data

KS3 Mathematics


D1.1 Planning a statistical enquiry

Contents


D1.2 Collecting data

D1.3 Organizing data

D1.4 Writing a statistical report


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, you may wish to investigate the lengths of words used in newspapers.

We could ask:

Do different types of newspaper use different length words?


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.


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 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 sample of people.

From an experiment involving observation, counting or measuring.


Sources of data


Choosing the sample

Once you have decided where the data will come from you must decide on the size and the type of the sample.

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.


Choosing the sample

It is important that the sample is representative of the group you are investigating.

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.


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?


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,

the sample size and type,



Contents


D1.4 Two-way tables




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 data collection sheet or observation sheet is used when recoding 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.


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.



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 +



For example : Did you see the Olympics on TV ?

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.



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.


How would you rate the leisure facilities available in your local area? Tick one box only.


A scale can be used when asking for an opinion.

For example,

Excellent UnsatisfactoryPoorSatisfactoryGood



5) Do not ask leading questions.

For example, this question conveys a particular opinion,

Don’t you agree that football is the best sport?

A better question is :

What one of the following sports do you like the best?

football rugby tennis golf cricket boxing


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:




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:



The intervals given overlap. Also, if a person has read more than 6 books there is nowhere to tick.

How many books did you read last month?

0-2 2-4 4-6


How many books did you read last month?Tick one box.

0-2 3-5 6-8 8+


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.


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.

For example, to investigate a claim that the amount of TV watched has an impact on weight we can use the following:

age sex height (cm) weight (kg) hours of TV watched per week


Using a tally chart

When collecting data that involves counting something we often use a tally chart.

For example, this tally chart can be used to record peoples’ 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


Using a tally chart



Contents

D1.4 Two-way tables





Using a frequency table

Once data has been collected it is often organized into a frequency table.

For example, 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


Categorical data

Categorical data is data that is non-numerical.

For example,

Sometimes categorical data can contain numbers.

favourite football team,

eye colour,

birth place.

For example, favourite number,

last digit in your telephone number,

most used bus route.


Discrete and continuous data

Discrete data can only take certain values.

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.


Discrete or continuous data


Grouping discrete data

A group of 20 people were ask 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.


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

£3.5434p£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.


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

£3.5434p£1.68 50p

82p£7.54£1.09 £2.81

£2.4346p£1.70 £1.29


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)




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




What is wrong with the class intervals in this grouped frequency table showing times?

5:30 ≤ time < 6:00

4:00 ≤ time < 5:30

3:00 ≤ time < 4:00

2:30 ≤ time < 3:00

2:00 ≤ time < 2:30

FrequencyTime (minutes:seconds)

4:00 ≤ time < 4:30

3:30 ≤ time < 4:00

3:00 ≤ time < 3:30

2:30 ≤ time < 3:00

2:00 ≤ time < 2:30

FrequencyTime (minutes:seconds)


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


D1.4 Writing a statistical report

Contents






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


The data collection cycle


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:

An introduction stating the purpose of the survey and any initial conjectures which you plan to investigate.

A description of what sources you were used including a justification of the type and size of any samples used.

Calculations, such as the mean, median and mode, the give an overall picture of the data.



Problems or ambiguities that arose during the course of the investigation and how you dealt with them.

A summery of the conclusions shown by the data, not forgetting to refer back to your initial conjecture.

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.

Tables or graphs of the results, using ICT as appropriate. (Remember to justify you choice of what is presented.)



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 handspan and foot length.

© Boardworks Ltd 2004 1 of 43 D1 Planning and collecting data KS3 Mathematics.

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Transcript of © Boardworks Ltd 2004 1 of 43 D1 Planning and collecting data KS3 Mathematics.