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

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© Boardworks Ltd of 43 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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© Boardworks Ltd of 43 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?

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© Boardworks Ltd of 43 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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© Boardworks Ltd of 43 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.

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© Boardworks Ltd of 43 Sources of data

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© Boardworks Ltd of 43 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.

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© Boardworks Ltd of 43 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.

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© Boardworks Ltd of 43 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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© Boardworks Ltd of 43 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,

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© Boardworks Ltd of 43 D1.2 Collecting data Contents D1.3 Organizing data D1.4 Two-way tables D1 Planning and collecting data D1.1 Planning a statistical enquiry

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© Boardworks Ltd of 43 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.

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© Boardworks Ltd of 43 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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© Boardworks Ltd of 43 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

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© Boardworks Ltd of 43 Designing a questionnaire For example : Did you see the Olympics on TV ? People could answer : YesNoNot much Only the best bits Once a daySometimes 4) If possible, write questions so that they have a specific answer.

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© Boardworks Ltd of 43 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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© Boardworks Ltd of 43 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. For example, ExcellentUnsatisfactoryPoorSatisfactoryGood

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© Boardworks Ltd of 43 Designing a questionnaire 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? footballrugbytennisgolfcricketboxing

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© Boardworks Ltd of 43 Suggest a better question How much do you weigh? This is too personal, also some people don’t know their weight. UnderweightAverage weightOverweight Would you consider yourself to be: A better question would be:

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© Boardworks Ltd of 43 Suggest a better question Most people use a deodorant, do you ? Which make of deodorant do you use ? Male: Female:SureImpulseDoveOtherNone LynxOtherAdidasSlazengerNone Please circle any that apply. This is a leading question and may offend people. A more useful question would be:

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© Boardworks Ltd of 43 Suggest a better question 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? A better question would be: How many books did you read last month? Tick one box

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© Boardworks Ltd of 43 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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© Boardworks Ltd of 43 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: agesexheight (cm)weight (kg)hours of TV watched per week

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© Boardworks Ltd of 43 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 snacktallyfrequency crisps fruit nuts sweets The tally marks are recorded, as responses are collected, and the frequencies are then filled in

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© Boardworks Ltd of 43 Using a tally chart

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© Boardworks Ltd of 43 D1.3 Organizing data Contents D1.4 Two-way tables D1.2 Collecting data D1 Planning and collecting data D1.1 Planning a statistical enquiry

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© Boardworks Ltd of 43 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 Chinese 8

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© Boardworks Ltd of 43 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.

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© Boardworks Ltd of 43 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, 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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© Boardworks Ltd of 43 Discrete or continuous data

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© Boardworks Ltd of 43 Grouping discrete data A group of 20 people were ask how much change they were carrying in their wallets. These were their responses: 34p £ p £6.36 £4.07 £2.97 £3.53 6p £ p £ p 82p £7.54 £1.09 £2.81 £ p £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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© Boardworks Ltd of 43 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 £ p £6.36 £4.07 £2.97 £3.53 6p £ p £ p 82p £7.54 £1.09 £2.81 £ p £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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© Boardworks Ltd of 43 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 £ p £6.36 £4.07 £2.97 £3.53 6p £ p £ p 82p £7.54 £1.09 £2.81 £ p £1.70 £1.29

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© Boardworks Ltd of 43 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 ≤ ≤ length ≤ 20 0 < length ≤ 10 FrequencyLength (cm) This is an open class interval. 30 ≤ length 20 ≤ length < ≤ length < 20 0 ≤ length < 10 FrequencyLength (cm)

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© Boardworks Ltd of 43 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 < < weight < < weight < < weight Weight (g)Frequency 0 ≤ weight < ≤ weight < ≤ weight < ≤ weight

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© Boardworks Ltd of 43 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 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)

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© Boardworks Ltd of 43 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 Eat a packed lunch Eat at home

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© Boardworks Ltd of 43 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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© Boardworks Ltd of 43 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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© Boardworks Ltd of 43 The data collection cycle

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© Boardworks Ltd of 43 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.

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© Boardworks Ltd of 43 Writing a statistical report 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.)

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© Boardworks Ltd of 43 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 handspan and foot length.

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