Transcript Document

Tables & Charts
S3.3
Frequency Tables / Relative Frequency
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Cumulative Frequency Table
Stem-leaf Diagrams
Back to Back Stem Leafs
Five Figure Summaries
Box Plots
Scatter Diagrams
18-Jul-15
Created by Mr. [email protected]
Starter Questions
S3.3
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Q1.
Does 5x2 – 16x + 3 factorise to
(5x - 1)(x – 3)
Q2. Change into £’s
€75
exchange rate £1  € 1.5
Q3. Convert to scientific notation 0.0675
18-Jul-15
Created by Mr. [email protected]
Aims of the Lesson
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S3.3
1. Understand the term
Frequency Table and Relative Frequency .
2. Construct a Frequency/Relative Frequency Table.
3. Interpret information from Tables.
18-Jul-15
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3
Frequency tables
Raw data can often appear untidy and difficult to understand.
Organising such data into frequency tables can make it much
easier to make sense of (interpret) the data.
Data
Tally
Frequency
llll represents a tally of 5
18-Jul-15
Sum of Tally is the Frequency
4
Frequency tables
Example 1. A tomato grower ideally wants his tomatoes
to have diameters of 60mm, but a diameter ranging from
58mm to 62mm will be acceptable. Organise the
diameters given below into a frequency table.
58
56
60
61
56
59
58
58
59
56
60
60
57
59
59
61
60
57
56
62
56
58
59
58
62
60
60
57
62
62
61
62
58
61
56
59
56
58
60
61
58
59
62
58
59
62
59
60
Lowest number 56
Highest number 62
18-Jul-15
Created by Mr. Lafferty
5
Frequency tables
58
X
57
60
61
56
X
59
58
58
59
X
56
60
60
57
X
59
59
61
Diameter
56
57
60
X
57
59
59
56
X
58
60
58
Tally
ll
58
l
l
59
l
60
l
62
60
59
57
60
59
61
62
58
61
59
59
60
58
60
61
58
59
62
58
59
62
59
60
Frequency
61
62
18-Jul-15
Created by Mr. Lafferty
6
58
X
X
57
60
X
61
X
Frequency Tables
Relative
Relative
56
59
57
60
56
62
60
58
X 58
X 59
X
X X X X X X X X 60
Frequency
Frequency
X 59
X 62
X
X 59
X 57
X 58
X X
X X
X 56
59
60 59
61 58
used with
always adds
58
60
59
59 61
62
59
X 60
X
X
X charts
X 59
X 60
X X
X 59
X Pie
up to 1 X
58
57 62
X 61
X 58
X 60
X
X 61
X 59
X 58
X X
X 59
X 60
Diameter
Tally
56
lll
3
Relative Frequency
3 ÷ 48 = 0.0625
57
llll
4
4 ÷ 48 = 0.0833
58
59
llll llll
llll llll lll
9
13
60
llll llll
10
9 ÷ 48 = 0.1875
13 ÷ 48 = 0.2708
10 ÷ 48 = 0.2083
61
llll
5
62
llll
4
Total
18-Jul-15
Frequency
5 ÷ 48 = 0.1042
4 ÷ 48 = 0.0833
R48
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7
Charts & Tables
S3.3
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Now try Ex 3.1
Q2
Ch6 MIA (page 108)
18-Jul-15
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Starter Questions
S3.3
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1. Find the mean, range and median for the set of data.
9, 1, 5, 5, 8, 2, 4, 6
Q2. Find the area for the shapes
(w - 2)
(x – 5)
7
(x – 3)
Q3. Write in standard form 0.008654
18-Jul-15
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Cumulative
Frequency Tables
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S3.3
Learning Intention
Success Criteria
1. To explain how to
construct a Cumulative
Frequency Table.
18-Jul-15
1. Add a third column to a
frequency table to create a
Cumulative Frequency Table.
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Cumulative
Frequency Tables
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S3.3
Example : This table shows the number
of eggs laid by a clutch of chickens each
day over a seven day period.
A third column is added to keep a
running total
(Cumulative Frequency Table).
This makes it easier to
get the total number of items.
You have 1 minute to come up
with a question you can easily
answer from the table.
18-Jul-15
Created by Mr. Lafferty Maths Dept.
Day
Freq.
(f)
Cum. Freq.
Total so far
1
2
2
2
3
5
3
1
6
4
6
12
5
5
17
6
8
25
7
4
29
Cumulative
Frequency Tables
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S3.3
Now try Ex 3.2
Ch6 (page 109)
18-Jul-15
Created by Mr. Lafferty Maths Dept.
Starter Questions
S3.3
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Q1.
Factorise
4x2 + 9x - 9
Q2.
Multiply out
(a)
Q3.
18-Jul-15
a(ab – a)
(b)
3 7

5 15
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-2a( b2 – a)
Stem Leaf Graphs
Construction of Stem-Leaf
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S3.3
Learning Intention
Success Criteria
1. To construct a Stem-Leaf
Graph / Dot Graph and
answer questions based on
it.
18-Jul-15
1. Construct and understand
the Key-Points of a StemLeaf Graph / Dot Graphs.
2. Answer questions based on
the graph.
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Stem Leaf Graphs
Construction of Stem and Leaf
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S3.3
A Stem – Leaf graph is another way of displaying information :
Ages
This stem and leaf graph shows
2 4 6 8
the ages of people waiting in a
3 0 1 3
queue at a post office
4 4 4 5 6 7 9
5 0 3 4 9
How many people in the queue? 20
6 1 4 5 6
How many people in their forties? 6
leaves
stem
n = 20 Key : 2 4 means 24
18-Jul-15
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Stem Leaf Graphs
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S3.3
We can
now answer
Construction
of Stem and Leaf
various questions
Example
: Construct
stem and leaf graph for the following
about
the adata.
weights in (kgs) :
Weight (kgs)
1 2 2 3 5 5
2 1 3 9
3 2 2
4 0 0 1 1
12 12
40 13
57 15
54 15
55
21
13 23
55 29
15 32 32
55
40
32 40
15 41 41
21 51
40
54
23 55
41 55
29 55
51 57
12
5
stem
1 4 5 5 5 7
leaves
n = 20 Key : 2 3 means 23
18-Jul-15
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Dot Plot
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S3.3
Weight (kgs)
We can convert stem leaf into a simple
Dot diagram by taking each level and
adding a dot for each leaf
1 2 2 3 5 5
2 1 3 9
3 2 2
4 0 0 1 1
5 1 4 5 5 5 7
leaves
stem
1
2
3
4
5
Charts & Tables
Stem Leaf & Dot Diagram
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S3.3
Now try Ex 4.1
Ch6 (page 112)
18-Jul-15
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Starter Questions
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S3.3
Explain why the statement below are true or
false.
Factorising x2 – 9 we get (x - 3)(x - 3)
Multiply out 4x – 2( 8 – x) = 2x -16
6 14 188
83
 
1
7 15 105 105
18-Jul-15
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Stem Leaf Graphs
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S3.3
Construction of Back to Back Stem-Leaf
Learning Intention
Success Criteria
1. To construct a Back to Back
Stem-Leaf Graph and
answer questions based on
it.
18-Jul-15
1. Construct and understand
the Key-Points of a Back
to Back Stem-Leaf Graph.
2. Answer questions based on
the graph.
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Stem Leaf Graphs
Back to Back Stem – Leaf Graphs
S3.3
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Rugby Team 1
Heights
A back to back stem-leaf
helps us to compare two
sets of data.
Write down a
question that can
be answered easily
from the graph.
18-Jul-15
4 2 1
7 6
8 5 0
6 43 3 1
7 0
n = 15
14
15
16
17
18
Rugby Team 2
Heights
0
3
0
1
1
2 6 7 8
4
1 6
6
4 4
n = 15
14 | 1 represents 141cm
Created by Mr. Lafferty Maths Dept.
Charts & Tables
S3.3
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Back to Back Stem Leaf Graphs
Now try Ex 4.2
Ch6 (page 113)
18-Jul-15
Created by Mr. Lafferty Maths Dept.
Starter Questions
S3.3
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1. Find two numbers that add to give -13
an multiply to give - 48.
2. Why does x + 8x +15 factorise to (x + 5) (x + 3)
2
3. Solve (2x + 8)2 = 4x2 .
18-Jul-15
Created by Mr. Lafferty Maths Dept.
Five Figure Summary
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S3.3
Learning Intention
Success Criteria
1. To explain the meaning
and show how to workout
the five figure summary
information for a set of
data.
1. Understand the terms
L , H, Q1, Q2 and Q3.
2. Be able to work
L , H, Q1, Q2 and Q3
For a set of data
18-Jul-15
Created by Mr. Lafferty Maths Dept.
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S3.3
Five Figure Summary
When a set of numbers are put in ORDER,
it can be summarised by quoting five figures.
1. The highest number
(H)
2. The lowest number
(L)
3. The median, the number that halves the list (Q2)
4. The upper quartile, the median of the upper half (Q3)
5. The lower quartile, the median of the lower half (Q1)
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S3.3
Five Figure Summary
Q2 = Median
Q1 = lower
(middle value)
Q3 = upper
middle
value
Example
Find the five figure summary
forvalue
the data.
middle
2, 4, 5, 5, 6, 7, 7, 7, 8, 9, 10
The 11 numbers are already in order !
Q1 = 5
2
4
5
Q2 = 7
5
6
7 7
Q3 = 8
7
L =2
18-Jul-15
8
9 10
H = 10
Created by Mr. Lafferty Maths Dept.
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S3.3
Five Figure Summary
Q2 = Median
Q1 = lower
(middle value)
Q3 = upper
middle
value
Example
Find the five figure summary
forvalue
the data.
middle
2, 4, 5, 5, 6, 7, 7, 8, 9, 10
The 10 numbers are already in order !
Q1 = 5
2
4
5
Q2 = 6.5
5
6
Q3 = 8
7 7
L =2
18-Jul-15
8
9 10
H = 10
Created by Mr. Lafferty Maths Dept.
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S3.3
Five Figure Summary
Q2 = Median
Q1 = lower
(middle value)
Q3 = upper
middle
value
Example
Find the five figure summary
forvalue
the data.
middle
2, 4, 5, 5, 6, 7, 8, 9, 10
The 9 numbers are already in order !
Q1 = 4.5
2
4
5
Q2 = 6
5
6
Q3 = 8.5
7 8
L =2
18-Jul-15
9 10
H = 10
Created by Mr. Lafferty Maths Dept.
Five Figure Summary
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S3.3
Now try Ex 5.1
Ch6 (page 115)
18-Jul-15
Created by Mr. Lafferty Maths Dept.
Starter Questions
S3.3
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1. Write the five figure summary for the data below.
3, 1, 5, 5, 8, 2, 4, 6
Q2. Find the area of the first shape and the
perimeter of the second shape.
(p - 2)
(y – 5)
9
18-Jul-15
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3
Box Plot
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S3.3
Learning Intention
Success Criteria
1. To show how to construct
a box plot using the five
figure summary.
18-Jul-15
1. Be able to construct a box
plot using the five figure
summary data.
Created by Mr. Lafferty Maths Dept.
Finding the median, quartiles and inter-quartile range.
Example 1: Find the median and quartiles for the data below.
12,
6,
4,
9,
8,
4,
9,
8,
5,
9,
8,
10
Order the data
Q2
Q1
4,
4,
5, 6,
Lower
Quartile
= 5½
8,
8,
Q3
8,
Median
= 8
9,
9,
9,
10,
Upper
Quartile
= 9
Inter- Quartile Range = 9 - 5½ = 3½
12
Finding the median, quartiles and inter-quartile range.
Example 2: Find the median and quartiles for the data below.
6,
3,
9,
8,
4,
10,
8,
4,
15,
8,
10
Order the data
Q2
Q1
3,
4,
4,
6,
Lower
Quartile
= 4
8,
8,
Median
= 8
Q3
8,
9,
10,
10,
Upper
Quartile
= 10
Inter- Quartile Range = 10 - 4 = 6
15,
Box and Whisker Diagrams.
Box plots are useful for comparing two or more sets of data like
that shown below for heights of boys and girls in a class.
Anatomy of a Box and Whisker Diagram.
Lower
Lowest
Quartile
Value
Whisker
4
5
Median
Upper
Quartile
Whisker
Box
6
7
Highest
Value
8
9
10
11
12
Boys
130
140
150
160
170
180
cm
Girls
190
Drawing a Box Plot.
Example 1: Draw a Box plot for the data below
Q2
Q1
4,
4,
5,
6,
8,
8,
Lower
Quartile
= 5½
4
5
Q3
8,
9,
Median
= 8
6
7
8
9,
9,
10,
Upper
Quartile
= 9
9
10 11
12
12
Drawing a Box Plot.
Example 2: Draw a Box plot for the data below
Q2
Q1
3,
4,
4,
6,
8,
Lower
Quartile
= 4
3
4
5
Q3
8,
8,
9,
7
8
10,
15,
Upper
Quartile
= 10
Median
= 8
6
10,
9
10 11
12 13
14 15
Drawing a Box Plot.
Question: Stuart recorded the heights in cm of boys in his
class as shown below. Draw a box plot for this data.
Q2
Q1
Q3
137, 148, 155, 158, 165, 166, 166, 171, 171, 173, 175, 180, 184, 186, 186
Lower
Quartile
= 158
130
140
Upper
Quartile
= 180
Median
= 171
150
160
170
180
cm
190
Drawing a Box Plot.
Question: Gemma recorded the heights in cm of girls in the same class and
constructed a box plot from the data. The box plots for both boys and girls
are shown below. Use the box plots to choose some correct statements
comparing heights of boys and girls in the class. Justify your answers.
Boys
130
140
150
160
170
180
cm
Girls
1. The girls are taller on average.
2. The boys are taller on average.
3. The girls show less variability in height.
4. The smallest person is a girl
5. The boys show less variability in height.
6. The tallest person is a boy
190
Box Plot
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S3.3
Now try Ex 6.1
Ch6 (page 117)
18-Jul-15
Created by Mr. Lafferty Maths Dept.
Starter Questions
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S3.3
1. Factorise x2 +11x+28
2. Explain why 2(x + 5) = x + 12 when x = 2
3. Is it true that
18-Jul-15
2
1
13
3
+ 2 5
3
5
15
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Scattergraphs
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S3.3
Construction of Scattergraphs
Learning Intention
Success Criteria
1. To construct a scattergraph
and answer questions based
on it.
1. Construct and understand
the Key-Points of a
scattergraph.
2. Know the term positive and
negative correlation.
18-Jul-15
Created by Mr. Lafferty Maths Dept.
S3.3
This scattergraph
shows the heights
and weights of a
sevens football team
Write down height and
Scattergraphs
weight of each player.
Construction of Scattergraph
180
Bob
Tim
160
Height (cm)
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Team
Sam
140
Joe
Gary
Jim
Dave
120
100
0
18-Jul-15
20
40
Weight (kg)
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60
Scattergraphs
S3.3
Construction of Scattergraph
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When two quantities are strongly connected we say there is a
strong correlation between them.
Best fit line
x x
x x
x x
Strong positive
correlation
18-Jul-15
x
x x
x
x
x
Best fit line
Strong negative
correlation
Created by Mr. Lafferty Maths Dept.
Draw in the
best fit line
Scattergraphs
Construction of Scattergraph
Car Price
Age (£1000)
1
1
9
8
2
3
3
3
4
4
5
8
7
6
5
5
4
2
18-Jul-15
12
Is there
a correlation?
If yes, what
kind?
10
Car prices (£1000)
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S3.3
8
6
4
2
0
0
2
4
6
Ages (Years)
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8
10
12
Scattergraphs
S3.3
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Construction of Scattergraphs
Now try Ex 7.1
Ch6 (page 120)
18-Jul-15
Created by Mr. Lafferty Maths Dept.