Volume of a cereal box
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Volume of a cereal box Populati on of a town Number of goals in a season Number of matches in a box Length of a crocodil e Shirt collar size Speed of a car Temperatu re of oven Discrete? Continuou s? Group the following as either discrete or continuous data.
description
Group the following as either discrete or continuous data. Speed of a car. Population of a town. Volume of a cereal box. Length of a crocodile. Shirt collar size. Discrete? Continuous?. Number of goals in a season. Number of matches in a box. Temperature of oven. Discrete. Continuous. - PowerPoint PPT Presentation
Transcript of Volume of a cereal box
Volume of a cereal
box
Population of a town
Number of goals in a
season
Number of matches in
a box
Length of a
crocodileShirt
collar size
Speed of a car
Temperature of oven
Discrete? Continuous?
Group the following as either discrete or continuous data.
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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
Top speed of a car
Temperature of oven
Discrete Continuous
Learning objectives:Learning objectives: To be able to design frequency
tables for discrete raw data; and and design data collection tables for design data collection tables for
gathering large discretegathering large discrete and and continuous sets of raw data, continuous sets of raw data,
choosing suitable class intervals.choosing suitable class intervals.
Learning objectives:Learning objectives: To be able to design frequency
tables for discrete raw data; and and design data collection tables for design data collection tables for
gathering large discretegathering large discrete and and continuous sets of raw data, continuous sets of raw data,
choosing suitable class intervals.choosing suitable class intervals.
Date: 04/06/2013Date: 04/06/2013
Title: Recording data in Title: Recording data in tablestables
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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.
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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.
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
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Grouping data
A list of results is called a data set.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?
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)
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 99.8 100.0 100.6100.6 101.1 101.4 101.4 101.5 101.6 101.6 101.8 101.9102.1 102.5 102.6 102.7 103.1 103.1 103.1 104.1 105.0105.2 105.6 105.6 105.7 105.8 105.9
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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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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
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”.
Notation for class intervals
100 ≤ t < 105
105 ≤ t < 110
95 ≤ t < 100
90 ≤ t < 95
85 ≤ t < 90
Times in seconds Frequency
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 99.8 100.0 100.6100.6 101.1 101.4 101.4 101.5 101.6 101.6 101.8 101.9102.1 102.5 102.6 102.7 103.1 103.1 103.1 104.1 105.0105.2 105.6 105.6 105.7 105.8 105.9
Class intervals
Use the data to fill in the table.
100 ≤ t < 105
105 ≤ t < 110
95 ≤ t < 100
90 ≤ t < 95
85 ≤ t < 90
Times in seconds Frequency
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 99.8 100.0 100.6100.6 101.1 101.4 101.4 101.5 101.6 101.6 101.8 101.9102.1 102.5 102.6 102.7 103.1 103.1 103.1 104.1 105.0105.2 105.6 105.6 105.7 105.8 105.9
Class intervals: Answer
Use the data to fill in the table.
19
7
28
5
1
.
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.
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
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
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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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.
Level 7
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..
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
