Tables

1
Tables Charts
Frequency Tables / Relative Frequency
Cumulative Frequency Table
Stem-leaf Diagrams
Back to Back Stem Leafs
Five Figure Summaries
Box Plots
Scatter Diagrams
2
Starter Questions
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
3
Aims of the Lesson

• Understand the term
• Frequency Table and Relative Frequency .
• 2. Construct a Frequency/Relative Frequency
  Table.
• 3. Interpret information from Tables.

4
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







Sum of Tally is the Frequency
5
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.
Lowest number
56
Highest number
62
6
Frequency tables
X
X
X
X
X
X
Diameter Tally Frequency
56
57
58
59
60
61
62
l
l
l
l
l
l
7
Relative Frequency always adds up to 1
Relative Frequency used with Pie charts
Frequency Tables
Diameter Tally Frequency
56
57
58
59
60
61
62
Total
Relative Frequency
3
3 48 0.0625
4
4 48 0.0833
9
9 48 0.1875
13
13 48 0.2708
10
10 48 0.2083
5
5 48 0.1042
4
4 48 0.0833
R48
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Charts Tables
Now try Ex 3.1 Q2 Ch6 MIA (page 108)
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Starter Questions
Q2. Find the area for the shapes
(w - 2)
(x 5)
(x 3)
7
Q3. Write in standard form 0.008654
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Cumulative Frequency Tables
Learning Intention
Success Criteria

1. Add a third column to a frequency table to create
   a Cumulative Frequency Table.

1. To explain how to construct a Cumulative
Frequency Table.
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Cumulative Frequency Tables
Example This table shows the number of eggs
laid by a clutch of chickens each day over a
seven day period.
Day Freq. (f)







Cum. Freq. Total so far
2
1
2
A third column is added to keep a running total
(Cumulative Frequency Table). This makes it
easier to get the total number of items.
3
2
5
1
3
6
6
4
12
You have 1 minute to come up with a question you
can easily answer from the table.
5
5
17
6
8
25
7
4
29
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Cumulative Frequency Tables
Now try Ex 3.2 Ch6 (page 109)
13
Starter Questions
Q1. Factorise 4x2 9x - 9
Q2. Multiply out (a) a(ab a) (b) -2a( b2
a)
Q3.
14
Stem Leaf Graphs
Construction of Stem-Leaf
Learning Intention
Success Criteria
1. Construct and understand the Key-Points of a
Stem-Leaf Graph / Dot Graphs.

1. To construct a Stem-Leaf Graph / Dot Graph and
   answer questions based on it.

2. Answer questions based on the graph.
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Stem Leaf Graphs
Construction of Stem and Leaf
A Stem Leaf graph is another way of displaying
information
Ages
This stem and leaf graph shows the ages of
people waiting in a queue at a post office
How many people in the queue?
20
How many people in their forties?
6
leaves
stem
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Stem Leaf Graphs
We can now answer various questions about the
data.
Construction of Stem and Leaf
Example Construct a stem and leaf graph for the
following weights in (kgs)
Weight (kgs)
1
2
2
12 12 13 15 15
21 23 29 32 32
40 40 41 41 51
54 55 55 55 57
12 40 57 54 55
13 55 15 32 55
32 15 41 21 40
23 41 29 51 12
2
leaves
stem
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Dot Plot
Weight (kgs)
2
2
1
We can convert stem leaf into a simple Dot
diagram by taking each level and adding a dot
for each leaf
2
leaves
stem
1
2
3
4
5
18
Charts Tables
Stem Leaf Dot Diagram
Now try Ex 4.1 Ch6 (page 112)
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Starter Questions
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
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Stem Leaf Graphs
Construction of Back to Back Stem-Leaf
Learning Intention
Success Criteria
1. Construct and understand the Key-Points of a
Back to Back Stem-Leaf Graph.

1. To construct a Back to Back Stem-Leaf Graph and
   answer questions based on it.

2. Answer questions based on the graph.
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Stem Leaf Graphs
Back to Back Stem Leaf Graphs
Rugby Team 2 Heights
Rugby Team 1 Heights
A back to back stem-leaf helps us to compare
two sets of data.
2
1
4
7
8
7
6
5
0
8
Write down a question that can be answered easily
from the graph.
3
1
3
4
6
7
0
n 15
n 15
14 1 represents 141cm
22
Charts Tables
Back to Back Stem Leaf Graphs
Now try Ex 4.2 Ch6 (page 113)
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Starter Questions
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Five Figure Summary
Learning Intention
Success Criteria

• Understand the terms
• L , H, Q1, Q2 and Q3.

1. To explain the meaning and show how to
workout the five figure summary information for a
set of data.

• Be able to work
• L , H, Q1, Q2 and Q3
• For a set of data

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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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Five Figure Summary
Q2 Median (middle value)
Q1 lower middle value
Q3 upper middle value
Example Find the five figure summary for the
data. 2, 4, 5, 5, 6, 7, 7, 7, 8, 9, 10
The 11 numbers are already in order !
7
8
5
Q3
Q2
Q1
7
L
H
10
2
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Five Figure Summary
Q2 Median (middle value)
Q1 lower middle value
Q3 upper middle value
Example Find the five figure summary for the
data. 2, 4, 5, 5, 6, 7, 7, 8, 9, 10
The 10 numbers are already in order !
8
Q3
Q2
Q1
6.5
5
L
H
10
2
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Five Figure Summary
Q2 Median (middle value)
Q1 lower middle value
Q3 upper middle value
Example Find the five figure summary for the
data. 2, 4, 5, 5, 6, 7, 8, 9, 10
The 9 numbers are already in order !
6
8.5
Q3
Q2
Q1
4.5
6
L
H
10
2
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Five Figure Summary
Now try Ex 5.1 Ch6 (page 115)
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Starter Questions
Q2. Find the area of the first shape and the
perimeter of the second shape.
(p - 2)
(y 5)
3
9
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Box Plot
Learning Intention
Success Criteria

1. Be able to construct a box plot using the five
   figure summary data.

1. To show how to construct a box plot using
the five figure summary.
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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
4, 4, 5, 6, 8, 8, 8, 9,
9, 9, 10, 12
Inter- Quartile Range 9 - 5½ 3½
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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
3, 4, 4, 6, 8, 8, 8,
9, 10, 10, 15,
Inter- Quartile Range 10 - 4 6
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Lower Quartile
Upper Quartile
Lowest Value
Highest Value
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Box Plot
Now try Ex 6.1 Ch6 (page 117)
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Starter Questions
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Scattergraphs
Construction of Scattergraphs
Learning Intention
Success Criteria

1. Construct and understand the Key-Points of a
   scattergraph.

1. To construct a scattergraph and answer questions
   based on it.

2. Know the term positive and negative
correlation.
42
This scattergraph shows the heights and weights
of a sevens football team
Scattergraphs
Write down height and weight of each player.
Construction of Scattergraph
Bob
Tim
Joe
Sam
Gary
Dave
Jim
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Scattergraphs
Construction of Scattergraph
When two quantities are strongly connected we say
there is a strong correlation between them.
Best fit line
Best fit line
Strong positive correlation
Strong negative correlation
44
Draw in the best fit line
Scattergraphs
Construction of Scattergraph
Is there a correlation? If yes, what kind?
Strong negative correlation
45
Scattergraphs
Construction of Scattergraphs
Now try Ex 7.1 Ch6 (page 120)