Group the following as either discrete or continuous data. 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 Temperature of oven Discrete? Continuous? Group the following as either discrete or continuous data.

Discrete Continuous Population of a town Volume of a cereal box Number of matches in a box Top speed of a car Length of a crocodile Shirt collar size Number of goals in a season Temperature of oven

Date: 04/06/2013 Title: Recording data in tables 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.

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.

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

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 13 6 3 8 The tally marks are recorded, as responses are collected, and the frequencies are then filled in.

What is the best size for the class intervals for the race times data? 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. On the next page the results are shown again to aid discussion. Ask pupils what the shortest and fastest times are. It is appropriate for the interval to be a multiple of 5 or 10 if possible. The best interval here would be 5 seconds. What is the best size for the class intervals for the race times 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 £1.72 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.

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 £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.

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 £3.54 £1.68 50p 82p £7.54 £1.09 £2.81 £2.43 46p £1.70 £1.29 Explain why class sizes of £5 would be inappropriate. Tell pupils that we should aim to have between five and ten class intervals, depending on the data. Could we use a class size of 20p?

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 Frequency Length (cm) 30 ≤ length 20 ≤ length ≤ 30 10 ≤ length ≤ 20 0 < length ≤ 10 Frequency Length (cm) 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.

class intervals The times roughly range from 85 to 110 seconds. 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 99.8 100.0 100.6 100.6 101.1 101.4 101.4 101.5 101.6 101.6 101.8 101.9 102.1 102.5 102.6 102.7 103.1 103.1 103.1 104.1 105.0 105.2 105.6 105.6 105.7 105.8 105.9 The times roughly range from 85 to 110 seconds. 110 – 85 = 25 seconds. Suppose we decide to use class intervals with a width of 5 seconds. 25 ÷ 5 = 5 class intervals

Notation for class intervals 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? Discuss where 90 and 105 should go. The table is ambiguous. For discrete data it would be possible to edit the table to say 86 – 90, 91 – 95, 96 – 100, 101 – 105 etc (or 85 – 89, 90 – 94 etc) but for continuous data this would not work.

Notation for class intervals Can you explain what the symbols in the middle column mean? 100 ≤ t < 105 105 ≤ t < 110 95 ≤ t < 100 90 ≤ t < 95 85 ≤ t < 90 Times in seconds 85 – 90 but not including 90 Frequency 90 – 95 but not including 95 95 – 100 but not including 100 100 – 105 but not including 105 Discuss where 90, 95 etc would go in this table. Represent the inequality on a number line. Ask pupils where numbers such as 99.9999999 would go. Note that the data has been rounded off to 1 d.p. so it could be argued that we could write the intervals as 85.0 – 89.9, 90.0 – 94.9 etc but this would imply that the data is discrete, so this would be incorrect. 105 – 110 but not including 110

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 “times larger than or equal to 90 seconds and less than 95 seconds” or “from 90 up to but not including 95”. 2) 105 ≤ t < 110 Pupils could work together in pairs to practise the correct use of vocabulary. “times larger than or equal to 105 seconds and less than 110 seconds” or “from 105 up to but not including 110”.

Notation for class intervals This activity involves pupils deciding which class interval a number belongs in. The numbers should be dragged into the right interval.

Use the data to fill in the table. 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 99.8 100.0 100.6 100.6 101.1 101.4 101.4 101.5 101.6 101.6 101.8 101.9 102.1 102.5 102.6 102.7 103.1 103.1 103.1 104.1 105.0 105.2 105.6 105.6 105.7 105.8 105.9 100 ≤ t < 105 105 ≤ t < 110 95 ≤ t < 100 90 ≤ t < 95 85 ≤ t < 90 Times in seconds Frequency Use the data to fill in the table. Pupils would benefit from having a print out of the data to avoid missing out data items. A tally could be used if required. They should check they have 60 items in total in the frequency column.

Class intervals: Answer 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 99.8 100.0 100.6 100.6 101.1 101.4 101.4 101.5 101.6 101.6 101.8 101.9 102.1 102.5 102.6 102.7 103.1 103.1 103.1 104.1 105.0 105.2 105.6 105.6 105.7 105.8 105.9 100 ≤ t < 105 105 ≤ t < 110 95 ≤ t < 100 90 ≤ t < 95 85 ≤ t < 90 Times in seconds Frequency 1 Use the data to fill in the table. 5 Pupils would benefit from having a print out of the data to avoid missing out data items. A tally could be used if required. They should check they have 60 items in total in the frequency column. 28 19 7

Which ones are you using? Creative Thinker Effective Participator Independent Enquirer Reflective Learner Self Manager Team Worker PLT Skills Which ones are you using? Learning objectives review 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. . I don’t understand I nearly understand I fully understand

Effective Participator Creative Thinker Effective Participator Independent Enquirer Reflective Learner Self Manager Team Worker 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. Assessment 6b 6a 7c - 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?

Level 6 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: Number of magazines Tally Frequency 0 - 4   5 - 9 10 - 14 15 - 19 20 - 24 25 - 29 30 - 34 35 - 39 40 - 44 45 - 49 more than 49

Level 7 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 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.

Which ones are you using? Creative Thinker Effective Participator Independent Enquirer Reflective Learner Self Manager Team Worker 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. Individual Assessment On your post it notes… Think about how you can improve your work. WWW (What Went Well) EBI (Even Better If)

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