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Volume of a cereal box Population of a town Number of goals in a season Number of matches in a box Length of a crocodile Shirt collar size Speed of a car Temperatur e of oven Discrete? Continuous? Group the following as either discrete or continuous data.

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2 of 53 2 of 43 Volume of a cereal box Population of a town Number of goals in a season Number of matches in a box Length of a crocodile Shirt collar size Top speed of a car Temperatur e of oven DiscreteContinuous

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Learning objectives: and design data collection tables for gathering large discrete and continuous sets of raw data, choosing suitable class intervals. Learning objectives: To be able to design frequency tables for discrete raw data; and design data collection tables for gathering large discrete and continuous sets of raw data, choosing suitable class intervals. Date: 04/06/2013 Title: Recording data in tables

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4 of 53 4 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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5 of 53 5 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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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. 13 6 3 8

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7 of 53 7 of 43 Grouping data A list of results is called a data set. It is often easier to analyze a large data set if we put the data into groups. These are called class intervals. A frequency diagram or histogram can then be drawn. You will need to decide on the size of the class interval so that there are roughly between 5 and 10 class intervals. What is the best size for the class intervals for the race times data?

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Grouping discrete data A group of 20 people were ask how much change they were carrying in their wallets. These were their responses: 34p £1.72 83p £6.36 £4.07 £2.97 £3.53 6p £9.54 34p £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 £3.54 34p £1.68 50p 82p £7.54 £1.09 £2.81 £2.43 46p £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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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 £1.72 83p £6.36 £4.07 £2.97 £3.53 6p £3.54 34p £1.68 50p 82p £7.54 £1.09 £2.81 £2.43 46p £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)

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class intervals The times roughly range from 85 to 110 seconds. Suppose we decide to use class intervals with a width of 5 seconds. 110 – 85 = 25 seconds. 25 ÷ 5 = 5 class intervals 88.4 91.5 92.1 93.3 93.9 94.7 95.0 95.3 95.5 95.6 95.6 96.3 96.5 96.9 97.0 97.0 97.0 97.3 97.4 97.4 97.7 97.8 98.0 98.2 98.2 98.4 98.4 98.5 98.9 99.0 99.1 99.6 99.6 99.8100.0100.6 100.6101.1101.4101.4101.5101.6101.6101.8101.9 102.1102.5102.6102.7103.1103.1103.1104.1105.0 105.2105.6105.6105.7105.8105.9

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13 of 53 13 of 43 How should the class intervals be written down? Times in seconds Frequency 85 – 90 90 – 95 95 – 100 100 – 105 105 - 110 What is wrong with this table? Notation for class intervals

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14 of 53 14 of 43 100 ≤ t < 105 105 ≤ t < 110 95 ≤ t < 100 90 ≤ t < 95 85 ≤ t < 90 Times in seconds 85 – 90 but not including 90 FrequencyTimes in seconds Can you explain what the symbols in the middle column mean? Notation for class intervals 100 – 105 but not including 105 105 – 110 but not including 110 95 – 100 but not including 100 90 – 95 but not including 95

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Notation for class intervals 85 ≤ t < 90 means “times larger than or equal to 85 seconds and less than 90 seconds” Another way to say this is “from 85 up to but not including 90” Can you say these in both ways? 1) 90 ≤ t < 95 2) 105 ≤ t < 110 “times larger than or equal to 90 seconds and less than 95 seconds” or “times larger than or equal to 105 seconds and less than 110 seconds” or “from 105 up to but not including 110”. “from 90 up to but not including 95”.

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Notation for class intervals

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100 ≤ t < 105 105 ≤ t < 110 95 ≤ t < 100 90 ≤ t < 95 85 ≤ t < 90 Times in secondsFrequency 88.4 91.5 92.1 93.3 93.9 94.7 95.0 95.3 95.5 95.6 95.6 96.3 96.5 96.9 97.0 97.0 97.0 97.3 97.4 97.4 97.7 97.8 98.0 98.2 98.2 98.4 98.4 98.5 98.9 99.0 99.1 99.6 99.6 99.8100.0100.6 100.6101.1101.4101.4101.5101.6101.6101.8101.9 102.1102.5102.6102.7103.1103.1103.1104.1105.0 105.2105.6105.6105.7105.8105.9 Class intervals Use the data to fill in the table.

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100 ≤ t < 105 105 ≤ t < 110 95 ≤ t < 100 90 ≤ t < 95 85 ≤ t < 90 Times in secondsFrequency 88.4 91.5 92.1 93.3 93.9 94.7 95.0 95.3 95.5 95.6 95.6 96.3 96.5 96.9 97.0 97.0 97.0 97.3 97.4 97.4 97.7 97.8 98.0 98.2 98.2 98.4 98.4 98.5 98.9 99.0 99.1 99.6 99.6 99.8100.0100.6 100.6101.1101.4101.4101.5101.6101.6101.8101.9 102.1102.5102.6102.7103.1103.1103.1104.1105.0 105.2105.6105.6105.7105.8105.9 Class intervals: Answer Use the data to fill in the table. 19 7 28 5 1

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. Learning objectives review I don’t understand I nearly understand I fully understand Effective Participator Self Manager Independent Enquirer Creative Thinker Team Worker Reflective Learner PLT Skills Which ones are you using? To be able to design frequency tables for discrete raw data; and design data collection tables for gathering large discrete and continuous sets of raw data, choosing suitable class intervals.

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Assessment Effective Participator Self Manager Independent Enquirer Creative Thinker Team Worker Reflective Learner Learning Objectives: To be able to design frequency tables for discrete raw data; and design data collection tables for gathering large discrete and continuous sets of raw data, choosing suitable class intervals. - Join up with another pupil. Discuss your answers to the task. - Have you both got the same answers? If not why? What level am I working at? 6b 6a 7c

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Number of magazines TallyFrequency 0 - 4 5 - 9 10 - 14 15 - 19 20 - 24 25 - 29 30 - 34 35 - 39 40 - 44 45 - 49 more than 49 The possible answers are likely to range from 0 to 100, so you might draw a tally chart with groupings similar to the one below: Level 6

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22 of 53 22 of 43 You are investigating the length of time each member of a class spends on the internet per week. Look at the class groupings below - do you think they are right? Time (h)Frequency 0 ≤ time ≤ 10 10 ≤ time ≤ 20 20 ≤ time ≤ 30 These groups are wrong, because the times of '10 hours' and '20 hours' can be entered into two different groups. For example, the time 10 hours can be entered into 0 ≤ time ≤10 (where time is less than or equal to 10 hours), and also into 10 ≤ time ≤ 20 (where time is more than or equal to 10 hours). Level 7

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Time (h)Frequency 0 < time < 10 10 < time < 20 20 < time < 30 These groups are also wrong, because the times '10 hours' and '20 hours' cannot be entered into any of the groups.For example, the time 10 hours can neither be entered into 0 < time < 10 (where time is less than 10 hours), nor can it be entered into 10 < time < 20 (where time is more than 10 hours). Time (h)Frequency 0 ≤ time < 10 10 ≤ time < 20 20 ≤ time < 30 These groupings are right. '10 hours' is included in the second group, but not the first and '20 hours' is included in the third group, but not the second. Level 7

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Individual Assessment Effective Participator Self Manager Independent Enquirer Creative Thinker Team Worker Reflective Learner PLT Skills Which ones are you using? Learning Objectives: To be able to design frequency tables for discrete raw data; and design data collection tables for gathering large discrete and continuous sets of raw data, choosing suitable class intervals. WWW (What Went Well) EBI (Even Better If) On your post it notes… Think about how you can improve your work. On your post it notes… Think about how you can improve your work.

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On your post it.. think about WWW (What did you enjoy in today's lesson?) EBI (This lesson would have been better If…) Effective Participator Self Manager Independent Enquirer Creative Thinker Team Worker Reflective Learner

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