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**D1 Planning and collecting data**

KS3 Mathematics The aim of this unit is to teach pupils to: Discuss a problem that can be addressed by statistical methods, and identify related questions to explore. Decide which data to collect and identify possible sources. Plan how to collect and organise the data and design suitable data collection sheets and tables. Collect and record data from primary and secondary sources. Communicate methods and results. Material in this unit is linked the Framework’s supplement of examples pp 248–255, 272 –274. D1 Planning and collecting data

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**D1.1 Planning a statistical enquiry**

Contents D1 Planning and collecting data D1 D1.1 Planning a statistical enquiry D1 D1.2 Collecting data D1 D1.3 Organizing data D1 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. A hypothesis is a statement of something that you believe to be true but do not have any evidence to support. 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?” Discuss the first steps in planning a statistical enquiry. Ask pupils to tell you what data is and establish that it can be both numerical (quantitative) and descriptive (qualitative). Discuss the definition of a hypothesis, giving examples. For example, we could hypothesize that tabloid newspapers use shorter words than broadsheet newspapers.

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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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**Data can be collected from a primary source or a secondary source.**

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: From a survey or questionnaire of a group of people. From an experiment involving observation, counting or measuring. Discuss possible sources of secondary data. Data from a secondary source is data that you have collected from somewhere else including the Internet, reference books or newspapers.

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Sources of data Decide whether the data shown is data that would come from an experiment, a survey, or from a secondary source.

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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. A sample is therefore choose to represent the group. How big should a sample be? The sample should be as large as possible. This will depend on the time and resources available. Discuss factors involved in selecting a representative sample group. If the sample size is too small, then the results will be unrepresentative.

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**Can you suggest a better sample?**

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? Discuss ways to ensure that a sample is representative. It would be unreasonable to ask a sample of people leaving a football ground for their favourite sport because most of these people would be football fans. If however we were investigating the eating habits of football fans this would be an ideal sample. When choosing a sample it is sensible to consider all the factors that may have an influence on the outcome. In this example, girls may prefer different sports to boys so either equal numbers of both sexes must be questioned or the data must be collected separately. 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? In weeks? In months? In years and months? In years? Discuss the fact that different units may be appropriate to different lines of enquiry. For example, if investigating the relationship of age and weight in newborn babies it would be appropriate to measure age in weeks or even days to take account of the fact that their height changes very rapidly. How will you measure height? In centimetres? In inches? In metres?

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**Planning a statistical enquiry**

Once you have decided on: 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, you can start the next stage which is to design a data collection sheet or questionnaire.

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**D1 Planning and collecting data**

Contents D1 Planning and collecting data D1 D1.1 Planning a statistical enquiry D1 D1.2 Collecting data D1 D1.3 Organizing data D1 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 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. Remind pupils that data that they collect themselves in a questionnaire or collection sheet is called primary data. Data can also be collected from secondary sources such as the Internet, newspapers or reference books.

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**Designing a questionnaire**

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. 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.

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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. How old are you? Do not ask : Tick one box for your age group. 15-20 21-25 26-30 31 + A better question is : Discuss what would be a better question for “How old are you?” before revealing a possible alternative.

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**Designing a questionnaire**

4) If possible, write questions so that they have a specific answer. Did you see the Olympics on TV? People could answer : Only the best bits No Sometimes Ask pupils for possible responses to this question before revealing them. Discuss what would be a better question for “Did you see the Olympics on TV?” before revealing a possible alternative on the next slide. Yes Once a day Not much

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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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**Designing a questionnaire**

A scale can be used when asking for an opinion. How would you rate the leisure facilities available in your local area? Tick one box only. Excellent Good Satisfactory Poor Unsatisfactory Before revealing the suggested scale ask pupils to discuss what scale of responses they would find appropriate.

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**Designing a questionnaire**

5) Do not ask leading questions. The question below conveys a particular opinion: Don’t you agree that football is the best sport? A better question is : Which one of the following sports do you like the best? football rugby tennis golf cricket boxing Emphasize that questions should not convey the questioner’s own opinion or indicate that one response would be preferable to another. Discuss what would be a better question for “Don’t you agree that football is the best sport?” before revealing a possible alternative.

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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. A better question would be: Underweight Average weight Overweight Would you consider yourself to be: Add that if you needed to know peoples’ weights exactly then an experiment involving measuring and recording would be more appropriate than a questionnaire.

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**Suggest a better question**

Most people use a deodorant, do you ? This is a leading question and may offend people. A more useful question would be: Which make of deodorant do you use ? Male: Female: Sure Impulse Dove Other None Lynx Adidas Slazenger Please circle any that apply.

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**Suggest a better question**

How many books did you read last month? 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+ Also, tell pupils that the intervals, unless they are open, should be of equal size.

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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? There isn’t a box to cover my answer. I don’t want to answer this question because it’s too personal. What does this question mean?

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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 Point out that the headings used in the sheet should include units where appropriate.

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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 13 6 3 Point out that the fifth tally mark is made by crossing through the previous four marks. This makes it easier to count them up. Define frequency as the number of times something occurs. 8 The tally marks are recorded, as responses are collected, and the frequencies are then filled in.

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Using a tally chart Use this tally chart to collect data from the class. For example, to find out the size of each person’s family.

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**D1 Planning and collecting data**

Contents D1 Planning and collecting data D1 D1.1 Planning a statistical enquiry D1 D1.2 Collecting data D1 D1.3 Organizing data D1 D1.4 Writing a statistical report

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**Categorical data is data that is non-numerical.**

For example: favourite football team eye colour birth place. Sometimes categorical data can contain numbers. For example: favourite number When we say that categorical data is non-numerical we mean that it is not counting anything or a measure of anything. Ask pupils to suggest other examples. Categorical data can be displayed in a pie chart or bar graph. last digit in your telephone number most used bus route.

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**Discrete and continuous data**

Numerical data can be discrete or continuous. Discrete data can only take certain values. For example: shoe sizes the number of children in a class the number of sweets in a packet. Continuous data comes from measuring and can take any value within a given range. Ask pupils to give further examples. For example: 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**

Use this activity to review the difference between discrete and 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 Define frequency as the number of times something occurs. In this example, the frequency represents the number of pupils who prefer that take-away.

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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 £1.72 83p £6.36 £4.07 £2.97 £3.53 6p £9.54 £1.68 50p 82p £7.54 £1.09 £2.81 £2.43 46p £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 £1.72 83p £6.36 £4.07 £2.97 £3.53 6p £9.54 £1.68 50p 82p £7.54 £1.09 £2.81 £2.43 46p £1.70 £1.29 We can use class sizes of £1: £ £1.00, £ £2.00, £ £3.00, £ £4.00, £ £5.00, Over £5. This is an open class interval.

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**Choosing appropriate class intervals**

£1.72 83p £6.36 £4.07 £2.97 £3.53 6p £9.54 £1.68 50p 82p £7.54 £1.09 £2.81 £2.43 46p £1.70 £1.29 Complete the following frequency table for this data: Amount of money (£) Frequency 7 5 3 Complete the table and suggest to pupils they can check their solutions by adding up the frequencies and making sure that the total is the same as the number of data items (20). 1 1 Over 5.00 3

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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. For the following data: 34p £1.72 83p £6.36 £4.07 £2.97 £3.53 6p £9.54 £1.68 50p 82p £7.54 £1.09 £2.81 £2.43 46p £1.70 £1.29 Tell pupils that we should aim to have between five and ten class intervals, depending on the data. Explain why class sizes of £5 would be inappropriate. Could we use a class size of 20p?

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**Grouping continuous data**

Continuous data is usually grouped into equal class intervals. The class intervals are written using the symbols ≤ and <. 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 Frequency Length (cm) 30 ≤ length 20 ≤ length ≤ 30 10 ≤ length ≤ 20 0 ≤ length ≤ 10 Frequency Length (cm) Revise the meanings of the inequality symbols used to describe the class intervals. Discuss the fact that the class intervals in this table overlap so that it would be possible to put 10 cm, 20 cm, and 30 cm in either of two groups. Click to reveal the table correctly. An alternative would be to have class intervals of: 0 < length ≤ 10 10 < length ≤ 20 20 < length ≤ 30 30 < length This is an open class interval.

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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 Note that 10 < weight < 20 means that the weights in this interval are greater than ten and less than 20. This interval does not include 10g or 20g. This time 10g, 20g, and 30g are not included in any of the class intervals. Click to reveal the table correctly. An alternative would be to have class intervals of: 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 Ask questions to ensure that pupils are able to extract information from a two-way table. For example: How many Year 9 pupils eat a packed lunch? (32) How many pupils eat school dinners? (102) How many pupils are there in Year 8? (85) How many more Year 8 pupils go home for lunch than Year 9 pupils? (4) What do most of the pupils asked do at lunch time? (Eat a packed lunch)

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**D1.4 Writing a statistical report**

Contents D1 Planning and collecting data D1 D1.1 Planning a statistical enquiry D1 D1.2 Collecting data D1 D1.3 Organizing data D1 D1.4 Writing a statistical report

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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 Interpret and discuss the results Collect the data from a variety of sources Discuss the data collection cycle, giving examples for each stage. Discuss the fact that when we examine the result at the end of a survey, new questions that were not anticipated during the planning stage are thrown up. These can be investigated further and so the cycle begins again. Process and display the data

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**The data collection cycle**

Use this activity to discuss the various stages involved in conducting a statistical enquiry.

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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: An introduction stating the purpose of the survey and any initial conjectures which you plan to investigate. A description of what sources were used including a justification of the type and size of any samples used. Use this and the following slide to summarize the main teaching points before pupils write the reports of their own statistical enquiries. Calculations, such as the mean, median and mode, to give an overall picture of the data.

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**Writing a statistical report**

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

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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. Remind pupils to start by writing down any hypotheses or conjectures for the problem, including any related questions that might affect the results. They should also include a description of their sample. If there any measurements are to be collected, include the units that will be used and the degree of accuracy used. Any graphs that pupils decide to use should include explanations of why they have chosen them. The examples shown do not require the use of secondary data. Modify these examples as appropriate for the group. Use of mobile phones among teenagers. The relationship between hand span and foot length.

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