1. Created by Mr. Lafferty@mathsrevision.com
Tables & Charts
Frequency Tables / Relative Frequency
Cumulative Frequency Table
Stem-leaf Diagrams
Back to Back Stem Leafs
Five Figure Summaries
Box Plots
Scatter Diagrams
1-Apr-17
Created by Mr.

2. Created by Mr. Lafferty@mathsrevision.com
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
1-Apr-17
Created by Mr.

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.
1-Apr-17
Created by Mr. Lafferty

4. Sum of Tally is the Frequency
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
Sum of Tally is the Frequency
1-Apr-17

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. 58 59 56 62 57 60 61
Lowest number 56
Highest number 62
1-Apr-17
Created by Mr. Lafferty

6. Frequency tables X X X X X X 58 60 56 59 57 61 62 Diameter Tally
1-Apr-17
Created by Mr. Lafferty

7. Relative Frequency used with
Pie charts
Frequency Tables
Relative Frequency always adds up to 1 58 60 56 59 57 61 62 X X X X X
Diameter
Tally
Frequency 56 57 58 59 60 61 62
Total
Relative Frequency
lll
llll 3
3 ÷ 48 = 4
4 ÷ 48 = 9
9 ÷ 48 = 13
13 ÷ 48 = 10
10 ÷ 48 = 5
5 ÷ 48 = 4
4 ÷ 48 =
R48
1-Apr-17
Created by Mr. Lafferty

8. Created by Mr. Lafferty@mathsrevision.com
Charts & Tables
Now try Ex 3.1 Q2
Ch6 MIA (page 108)
1-Apr-17
Created by Mr.

9. Created by Mr. Lafferty Maths Dept.
Starter Questions
Q2. Find the area for the shapes
(w - 2)
(x – 5)
(x – 3) 7
Q3. Write in standard form
1-Apr-17
Created by Mr. Lafferty Maths Dept.

10. Cumulative Frequency Tables
Learning Intention
Success Criteria
1. To explain how to construct a Cumulative Frequency Table.
Add a third column to a frequency table to create a Cumulative Frequency Table.
1-Apr-17
Created by Mr. Lafferty Maths Dept.

11. 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 1 2 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. 2 3 5 3 1 6 4 6 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
1-Apr-17
Created by Mr. Lafferty Maths Dept.

12. Cumulative Frequency Tables
Now try Ex 3.2
Ch6 (page 109)
1-Apr-17
Created by Mr. Lafferty Maths Dept.

13. Created by Mr. Lafferty@mathsrevision.com
Starter Questions
Q1. Factorise
4x2 + 9x - 9
Q2. Multiply out
(a) a(ab – a) (b) -2a( b2 – a)
Q3.
1-Apr-17
Created by Mr.

14. Created by Mr. Lafferty Maths Dept.
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.
To construct a Stem-Leaf Graph / Dot Graph and answer questions based on it.
2. Answer questions based on the graph.
1-Apr-17
Created by Mr. Lafferty Maths Dept.

15. Created by Mr. Lafferty Maths Dept.
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 2 4 6 8 3 1 4 5 6 7 9 5 3 4 9
How many people in the queue? 20 6 1 4 5
How many people in their forties? 6
stem
leaves
n = 20 Key : means 24
1-Apr-17
Created by Mr. Lafferty Maths Dept.

16. 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 1 3 9 2 4 5 7 2 2 12 13 15 21 23 29 32 40 41 51 54 55 57 12 40 57 54 55 13 15 32 41 21 23 29 51 2 3 4 5
stem
leaves
n = 20 Key : means 23
1-Apr-17
Created by Mr. Lafferty Maths Dept.

17. Dot Plot We can convert stem leaf into a simple
Weight (kgs) 1 2 2 1 3 9 4 5 7 2
We can convert stem leaf into a simple
Dot diagram by taking each level and
adding a dot for each leaf 2 3 4 5
stem
leaves 1 2 3 4 5

18. Created by Mr. Lafferty Maths Dept.
Charts & Tables
Stem Leaf & Dot Diagram
Now try Ex 4.1
Ch6 (page 112)
1-Apr-17
Created by Mr. Lafferty Maths Dept.

19. Created by Mr. Lafferty@mathsrevision.com
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
1-Apr-17
Created by Mr.

20. Created by Mr. Lafferty Maths Dept.
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.
To construct a Back to Back Stem-Leaf Graph and answer questions based on it.
2. Answer questions based on the graph.
1-Apr-17
Created by Mr. Lafferty Maths Dept.

21. Stem Leaf Graphs A back to back stem-leaf helps us to compare two
Back to Back Stem – Leaf Graphs
Rugby Team 1
Heights
Rugby Team 2
Heights
A back to back stem-leaf
helps us to compare two
sets of data. 4 2 1 14 2 6 7 8 7 6 15 3 4 8 5 16 1 6
Write down a question that can be answered easily from the graph. 6 4 3 3 1 17 1 6 7 18 1 4
n = 15
n = 15
14 | 1 represents 141cm
1-Apr-17
Created by Mr. Lafferty Maths Dept.

22. Created by Mr. Lafferty Maths Dept.
Charts & Tables
Back to Back Stem Leaf Graphs
Now try Ex 4.2
Ch6 (page 113)
1-Apr-17
Created by Mr. Lafferty Maths Dept.

23. Created by Mr. Lafferty Maths Dept.
Starter Questions
1-Apr-17
Created by Mr. Lafferty Maths Dept.

24. Created by Mr. Lafferty Maths Dept.
Five Figure Summary
Learning Intention
Success Criteria
1. To explain the meaning and show how to workout the five figure summary information for a set of data.
Understand the terms
L , H, Q1, Q2 and Q3.
Be able to work
L , H, Q1, Q2 and Q3
For a set of data
1-Apr-17
Created by Mr. Lafferty Maths Dept.

25. 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)

26. Five Figure Summary 2 4 5 6 7 7 8 9 10 5 7 8 L = 2 H = 10
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 !
Q1 = 5
Q2 = 7
Q3 = 8 2 4 5 6 7 7 8 9 10
L = 2
H = 10
1-Apr-17
Created by Mr. Lafferty Maths Dept.

27. Five Figure Summary 2 4 5 6 7 8 9 10 5 6.5 8 L = 2 H = 10
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 !
Q1 = 5
Q2 =
6.5
Q3 = 8 2 4 5 6 7 8 9 10
L = 2
H = 10
1-Apr-17
Created by Mr. Lafferty Maths Dept.

28. Five Figure Summary 2 4 5 6 7 8 9 10 4.5 6 8.5 L = 2 H = 10
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 !
Q1 =
4.5
Q2 = 6
Q3 =
8.5 2 4 5 6 7 8 9 10
L = 2
H = 10
1-Apr-17
Created by Mr. Lafferty Maths Dept.

29. Created by Mr. Lafferty Maths Dept.
Five Figure Summary
Now try Ex 5.1
Ch6 (page 115)
1-Apr-17
Created by Mr. Lafferty Maths Dept.

30. Created by Mr. Lafferty Maths Dept.
Starter Questions
Q2. Find the area of the first shape and the perimeter of the second shape.
(p - 2)
(y – 5) 3 9
1-Apr-17
Created by Mr. Lafferty Maths Dept.

31. Created by Mr. Lafferty Maths Dept.
Box Plot
Learning Intention
Success Criteria
1. To show how to construct a box plot using the five figure summary.
Be able to construct a box plot using the five figure summary data.
1-Apr-17
Created by Mr. Lafferty Maths Dept.

32. Inter- Quartile Range = 9 - 5½ = 3½
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
Lower Quartile = 5½ Q1
Median = 8 Q2
Upper Quartile = 9 Q3
4, 4, 5, 6, 8, 8, , 9, , 9, 10, 12
Inter- Quartile Range = 9 - 5½ = 3½

33. Inter- Quartile Range = 10 - 4 = 6
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
Lower Quartile = 4 Q1
Median = 8 Q2
Upper Quartile = 10 Q3
3, 4, 4, 6, 8, , , , , 10, 15,
Inter- Quartile Range = = 6

34. Box and Whisker Diagrams.
130
140
150
160
170
180
190
Boys
Girls cm
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.
Lowest Value
Lower Quartile
Upper Quartile
Highest Value
Median
Whisker
Box 4 5 6 7 8 9 10 11 12

35. Lower Quartile = 5½ Upper Quartile = 9 Median = 8
4, 4, 5, 6, 8, 8, 8, 9, 9, 9, 10, 12
Example 1: Draw a Box plot for the data below
Drawing a Box Plot.
Lower Quartile = 5½ Q1
Upper Quartile = 9 Q3
Median = 8 Q2 4 5 6 7 8 9 10 11 12

36. Upper Quartile = 10 Lower Quartile = 4 Median = 8
3, 4, 4, 6, 8, 8, 8, 9, , 10, 15,
Example 2: Draw a Box plot for the data below
Drawing a Box Plot.
Upper Quartile = 10 Q3
Lower Quartile = 4 Q1
Median = 8 Q2 3 4 5 6 7 8 9 10 11 12 13 14 15

37. Upper Quartile = 180 Lower Quartile = 158 Median = 171
Question: Stuart recorded the heights in cm of boys in his class as shown below. Draw a box plot for this data.
Drawing a Box Plot.
137, 148, 155, 158, 165, 166, 166, 171, 171, 173, 175, 180, 184, 186, 186
Upper Quartile = 180 Q3
Lower Quartile = 158 Q1
Median = 171 Q2
130
140
150
160
170
180
190 cm

38. 2. The boys are taller on average.
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.
Drawing a Box Plot.
130
140
150
160
170
180
190
Boys
Girls cm
1. The girls are taller on average.
3. The girls show less variability in height.
5. The boys show less variability in height.
4. The smallest person is a girl
6. The tallest person is a boy

39. Created by Mr. Lafferty Maths Dept.
Box Plot
Now try Ex 6.1
Ch6 (page 117)
1-Apr-17
Created by Mr. Lafferty Maths Dept.

40. Created by Mr. Lafferty Maths Dept.
Starter Questions
1-Apr-17
Created by Mr. Lafferty Maths Dept.

41. Created by Mr. Lafferty Maths Dept.
Scattergraphs
Construction of Scattergraphs
Learning Intention
Success Criteria
Construct and understand the Key-Points of a scattergraph.
To construct a scattergraph and answer questions based on it.
2. Know the term positive and negative correlation.
1-Apr-17
Created by Mr. Lafferty Maths Dept.

42. Scattergraphs Construction of Scattergraph
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
1-Apr-17
Created by Mr. Lafferty Maths Dept.

43. Created by Mr. Lafferty Maths Dept.
Scattergraphs
Construction of Scattergraph
When two quantities are strongly connected we say there is a
strong correlation between them.
Best fit line x x
Best fit line
Strong positive
correlation
Strong negative
correlation
1-Apr-17
Created by Mr. Lafferty Maths Dept.

44. Scattergraphs Construction of Scattergraph Draw in the best fit line
Is there
a correlation?
If yes, what kind?
Age
Car Price
(£1000) 3 1 2 4 5 9 8 7 6
Strong negative correlation
1-Apr-17
Created by Mr. Lafferty Maths Dept.

45. Created by Mr. Lafferty Maths Dept.
Scattergraphs
Construction of Scattergraphs
Now try Ex 7.1
Ch6 (page 120)
1-Apr-17
Created by Mr. Lafferty Maths Dept.