Data Display
SLO: To draw a tally chart
Copy into
note book:
Tally Charts
Tally charts are used to organise data.
Data
Red
Tally
llll
Yellow
llll llll
llll ll
White
llll ll
Orange
l
Green
llll represents a tally of 5
Example: Organise the diameters of
tomatoes given below into a tally chart.
58 56 59 57 60 56 62 62 58 56 58 59
56 59 56 59 57 58 60 62 61 58 59 62
Step 1: Identify the largest and smallest values
Lowest number 56
Highest number 62
58
X 59
X 56
X 57
X 60
X 56
X 62
X 59
X 56
X
X 62
X 58
X 58
X 61
X 62
X
X 57
X 58
X 59
X 62
56
X 58
X 56
X 59
X 59
X 60
Step 2: Draw a tally chart from smallest to largest
Step 3: Fill in the tally chart
56
57
58
59
Tally
lll
ll l
llll
llll
61
llll
l
62
ll
60
l
Diameter
SLO:
How to make a frequency table
Frequency Tables
Copy into
note book:
A frequency is a tally chart with an extra column
for the total (frequency) of each tally.
Diameter
Tally
Frequency
Red
lll
3
Blue
llll
4
llll llll
llll llll lll
9
13
Green
Black
Web resources:
http://www.youtube.com/watch?v=Ng3SMd-_ys8
(Video: How to draw a tally graph and frequency table)
http://www.bbc.co.uk/bitesize/ks2/maths/data/frequency_diagrams/play/
(interactive frequency table questions)
SLO:
To be able to tell the difference
between a bar graph and a histogram
Copy into
your notes:
Bar Graphs
The bars of a bar chart do not touch each other (like the
bars in a jail)
Copy into
your notes
Histograms
The bars of a histogram touch each other.
A histogram is usually for grouped data.
Age Group
Frequency
1-5
4
6 - 10
16 - 20
30
27
50
21 - 25
11
11 - 15
Your Turn:
Is each of the following a histogram or a bar graph?
A
D
G
B
E
H
C
F
I
Web resources:
http://www.youtube.com/watch?v=g1wUk-JV7JU&feature=related
(You tube video explanation of how to draw a histogram)
SLO:
To draw a dot plot
Copy into
note book
Drawing Dot Plots
Step 1: Draw a number line from smallest to largest value
Step 2: Transfer each number to a dot on the number line
12, 12, 13, 15, 15, 21, 23, 29, 32, 32, 40, 40, 41, 41, 51, 54, 55, 55, 55, 57
10
20
30
40
50
60
Web resources:
http://www.youtube.com/watch?v=_zurDAF1Fw4
(You tube video explanation of dot plots)
http://www.learner.org/courses/learningmath/data/sessi
on2/part_b/making.html (interactive but not exciting)
SLO:
To read values from dot plots
Copy into
note book
Reading Dot Plots
The highest column of dots shows which
was most common i.e. 28 raisins.
The left
hand dot
shows the
smallest
value i.e.
25 raisins
The column
on the right
shows the
largest value
i.e.
31 raisins
Your Turn:
Number of pens in a pencil case
1) What was the is the most common number of pens?
8
2) How many pens did the students with the most pens have?
9
3) How many pens did the student with the least pens have?
5
Your Turn:
Number of people living in a house
1) What was the is the most common number of
people lining in a house? 4
2) How many people in the house with the most people? 6
3) How many people in the house with the least number 2
of people?
Your Turn:
Age of people at a party
1) How old was the youngest person at the party? 7
2) What was the most common age of the person at the party? 18
3) How old was the oldest person at the party? 72
Your Turn:
Scores of two classes in a test
1) Which class had the highest scoring student? 2
2) What was the most common score in class 1? 86
3) What was the lowest score in either class? 81
Your Turn:
Lengths of Male Bears
1) What was the most common weight of a male bear? 64
2) How long was the longest male bear? 83
3) How long was the shortest bear? 37
SLO:
To know what a stem and leaf are
Copy into
note book
Leaf: The last digit on the right of the number.
Stem: The digit or digits that remain when the leaf is dropped.
E.g.
Stem
284
Leaf
Your Turn:
For the following numbers identify which part is the stem
and which part is the leaf.
754
Stem
Leaf
67
Stem Leaf
123
Stem Leaf
7851
Stem
Leaf
Copy into
note book
What is a Stem and leaf Plot?
A stem and leaf plot is made up from two parts.
1)
All the
stem
numbers
in order
2)
All the leaf
numbers in
order
SLO:
To plot a stem and leaf graph
Here are the scores from two maths classes.
Class 1:
77 79 85 58 97 94 82 81 75 63 60 92 75 98 83 58 72 57
70 81
Class 2:
57 60 88 85 79 70 65 98 97 59 58 65 62 77 77 75 73 69
82 81
Quickly looking at the two sets of data it is hard to see
how well the two classes have done
Class 1: 76 79 85 58 97 94 82 81 75 63 60 92 75
Notice that in the data the least number is
98 83 58 72 57 70 81
Stem Leaf
5 8 8 7
57 and the greatest number is 98 so create
the stem by listing numbers from 5-9.
6
3 0
5
7 8 8
7
6 9 5 5 20
6
0 3
8
5 2 1 3 1
7
0 2 5 5 6 9
9
7 4 2 8
8
1 1 2 3 5
9
2 4 7 8
1:
Draw
anleaf
empty
stem
and
diagram
the
leaf
side
in leaf
order
(least to greatest)
Step
Step 4:
3:
2: Rearrange
Fill
Fill the
the
stem
side
side
Notes to copy:
Stem and Leaf plots are used to show data more clearly
Step 1: Draw an empty stem and leaf diagram
Step 2: Fill in the stem
Step 3: Fill in the leaves
Step 4: Rearrange the leaf side in order (least to greatest)
Class 2: 57 60 88 85 79 70 65 98 97 59 58 65 62
77 77 75 73 69 82 81
5 7 9 8
5
7 8 9
6 0 5 5 2 9
6
0 2 5 5 9
7 9 0 7 7 5 3
7
0 3 5 7 7 9
8 8 5 2 1
8
1 2 5 8
9 8 7
9
7 8
3:
1:Rearrange
Fill
Draw
the
leaves
empty
stem
leaf diagram
Step
Step 4:
2:
Fill
thean
stem
the leaf
sideand
in order
(least to greatest)
Plot a stem and leaf plot for the following data
Age of United states Presidents at their First
Inauguration: 57 61 57 57 58 57 61 54 68 51 49
64 50 48 65 52 56 46 54 49 50 47 55 54 42
51 56 55 51 54 51 60 62 43 55 56 61 52
69 64 (Through the 40th presidency)
4 9 8 6 9 7 2 3
5
7 7 7 8 7 4 1 0 2 6 4 0 5 4 1 6 5 1 4 1 5 6 2
6
1 1 8 4 5 0 2 19 4
Rearrange the leaf in numerical order from least to greatest
4
2 3 6 7 8 9 9
5
0 0 1 1 1 1 2 2 4 4 4 4 5 5 5 6 6 6 7 7 7 7 8
6
0 1 1 1 2 4 4 5 8 9
Construct a stem and leaf graph for the following weights in (kg)
12 12 13 15 15
21 23 29 32 32
40 40 41 41 51
54 55 55 55 57
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
Web resources:
http://www.youtube.com/watch?v=Gn4Izx_o7Pg
(You tube video explanation of stem and leaf plots)
http://www.wisc-online.com/Objects/ViewObject.aspx?ID=tmh1101
(individual interactive notes )
http://www.learner.org/courses/learningmath/data/session3/part_a/making.html
(individual interactive stem and leaf plot at bottom of page
but not very exciting )
SLO:
To read values from a stem
and leaf plot
1. How many presidents were 51 years old at their
4
inauguration?
42
2. What age is the youngest president to be inaugurated?
3. What is the age of the oldest president to be inaugurated? 69
4. How many presidents were 40-49 years old at their
inauguration? 7
4
2 3 6 7 8 9 9
5
0 0 1 1 1 1 2 2 4 4 4 4 5 5 5 6 6 6 7 7 7 7 8
6
0 1 1 1 2 4 4 5 8 9
Fill in the blanks
a) The lowest mark from either classes was 57
b) The highest score from either class was 98.
c) There were more higher scores in class 1
d) The most common score was in the 70’s for both classes
Class 1
5 7 7 8
6
7
0 3
0 2 5 5 6 9
8
1 1 2 3 5
9
2 4 7 8
Class 2
5 7 8 9
6 0 2 5 5 9
7
0 3 5 7 7 9
8
1 2 5 8
9
7 8
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
How old was the eldest person in the queue? 66
Ages
2
3
4
5
6
4
0
4
0
1
6
1
4
3
4
8
3
5 6 7 9
4 9
5 6
Extension:
Back to Back Stem and Leaf
Sometimes to compare two sets of data two sets of
leaves can share the same stem as below.
Rugby Team 1
Heights (cm)
A back to back stem-leaf
helps us to compare two
sets of data.
4 2 1
7 6
8 5 0
6 43 3 1
7 0
How tall was the tallest player?
14
15
16
17
18
187 cm
How short was the shortest player? 140 cm
Rugby Team 2
Heights (cm)
0
3
0
1
1
2 6 7 8
4
1 6
6
4 4
SLO: To plot a Scatter Graph
How Study Time Affects Grades
Weight Loss Over Time
250
120
Overall grade
100
200
Weight
150
Weight
100
80
60
40
20
0
0
0.5
1
1.5
2
2.5
3
3.5
50
Time in hours
0
2
4
6
8
10
12
Fat Grams and Calories in Food
Da ys w orke d out pe r month
700
600
Total Calories
0
500
400
300
200
100
0
0
5
10
15
20
25
Total Fat Grams
30
35
40
4
4.5
5
Scatter Plots
Scatter plots are similar to line graphs in that each graph
uses the horizontal ( x ) axis and vertical ( y ) axis to
plot data points.
Scatter plots are most often used to show correlations or
relationships among data.
How Study Time Affects Grades
120
Overall grade
100
80
60
40
20
0
0
0.5
1
1.5
2
2.5
3
Time in hours
3.5
4
4.5
5
Scatter plot for students height and weight
Copy into note book:
Step 1: Draw a pair of axis (you do not need to start at zero)
Step 2: Label the graph
Step 3: Plot the points from the table
(do not joint the dots up)
Student Height and Weight
Weight
1.3 m
53 kg
1.4 m
60 kg
1.2 m
55 kg
1.7 m
75 kg
1.6 m
69 kg
1.8 m
73 kg
1.5 m
68kg
80
Weight (kg)
Height
70
60
50
1.2 1.4 1.6 1.8
Height (m)
Web resources:
http://www.youtube.com/watch?v=soi-1wXQLoM&feature=channel&list=UL
(video: explanation of scatter plots)
Line of Best Fit
A line of best fit may also be called a trend line.
The line is straight and in the middle of the dots
Fat Grams and Calories in Food
700
Total Calories
600
500
400
300
200
100
0
0
5
10
15
20
25
Total Fat Grams
30
35
40
Web resources:
http://staff.argyll.epsb.ca/jreed/math9/strand4/scatterPlot.htm
(interactive line of best fit, use second graph down, ok for
teaching)
SLO: To recognise outliers
A outlier is a piece of data that is further
away from the trend line than the other data
What can you tell me
about this person?
What can you
tell me about
this person?
What can you tell me
about this person?
Weight Loss Over Time
250
200
Weight
150
W eight
100
50
0
0
2
4
6
8
10
Da ys w orke d out pe r month
What can you tell me
about this person?
12
Box and Whisker Graphs
SLO: Know the words
Quartile and Median
1st
Quartile
2nd
Quartile
3rd
Quartile
¼
¼
¼
¼
Q1
Lower
Quartile
½
Q2
Median
4th
Quartile
¼
¾
Q3
Upper
Quartile
SLO: Know how to find the:
Lower Quartile
Upper Quartile
Median
Before plotting box and whisker plots we need 5 pieces of information.
(Lowest, Highest, Lower Quartile, Upper Quartile and Median)
Find the lowest, highest, lower quartile, upper quartile
and median for the data.
9, 4, 5, 2, 5, 6, 7, 10, 7, 8, 7
Put the numbers in order
Q1 = 5
Q2 = 7
2 4 5 5 6 7 7
Lowest =2
Q3 = 8
7
8
9 10
Highest =10
Copy into note book:
To find values needed to draw a box and whisker diagram
2 4 6 7 8 9 13 14 15 24 56
Lower
Quartile
Median
Upper
Quartile
Step 1: Put the data in order
Step 2: Find the middle piece of data (Median)
Step 3: Find the ‘middle’ piece of data on the left (lower quartile)
Step 4: Find the ‘middle’ piece of data on the right (upper quartile)
Step 5: Find the smallest piece of data.
Step 6: Find the biggest piece of data
Your Turn:
Find the lowest, highest, lower quartile, upper quartile
and median for the data.
13, 8, 10, 1, 4, 15, 9, 12, 7, 3, 9
Put the numbers in order
Q1= 4
Q2= 9
Q3=12
1 3 4 7 8 9 9 10 12 13 15
Lowest= 1
Highest=15
Your Turn:
Find the lowest, highest, lower quartile, upper
quartile and median for the data.
7, 3, 5, 6, 7, 9, 15, 5, 4, 8
Put the numbers in order !
Q1 = 5
Q2 = 6.5
Q3 = 8
3 4 5 5 6 7 7
L =3
8
9 15
H = 15
Your Turn:
Find the lowest, highest, lower quartile, upper quartile
and median for the data.
5, 22, 1, 4, 6, 8, 9, 5, 7
Put the numbers in order !
Q1 = 4.5
Q2 = 6
Q3 = 8.5
1 4 5 5 6 7 8
L =1
9 22
H = 22
Your Turn:
Find the lowest, highest, lower quartile, upper
quartile and median for the following.
Lowest
Lower
Quartile
Median
Upper
Quartile
Highest
A
3 5 7 12 16 24 27 30 34 39 42
3
7
24
34
42
B
1 4 5 6 8 10 27 30 43 48 70
1
5
10
43
70
C
4 9 12 17 19 26 30
4
9
17
26
30
D
83 62 13 40 87 23 80
13
23
62
83
87
E
19 9 4 8 2 17 31 4 12 10 3
2
4
9
17
31
F
1 1 2 2 3 3 3 4 4 5 5 5 7 8 8
1
2
4
5
8
G
1 3 7 8 9 10 16 22 24 35
1
7
9.5
22
35
H
2 6 8 12 14 17 19 20
2
7
13
18
20
I
47 40 34 38 43 50 18 30
18
32
39
45
50
Question
2 14
17
Data
SLO:
To draw a box and whisker diagram
Box and Whisker Diagrams.
Copy this into your note book
Lower
Lowest
Quartile
Value
Whisker
4
5
6
Median
Upper
Quartile
Whisker
Box
7
Highest
Value
8
9
10
11
12
Copy into
note book
Drawing Box and Whisker
Diagrams.
:
Given the following data, plot a box and whisker plot
Median = 12
Lowest = 6 Lower Quartile = 10
Highest = 21
Upper Quartile = 18
Step 1: Draw a number line from lowest to highest
Step 2: Draw 5 small vertical lines at the 5 data points
Step 3: Join lines to make Box and whisker
6
8
10
12
14
16
18
20
22
Drawing Box and Whisker
Diagrams.
Draw a box and Whisker diagram for the following data.
6,
3,
9,
8,
4,
10,
8,
4,
15,
8,
10
Step 1: Order the data
Step 2: Find the 5 data points Q2, Q1, Q3, Min, Max
3,
Lowest
= 3
4,
4,
Lower
Quartile
= 4
Q3
Q2
Q1
Min
6,
8,
8,
Median
= 8
8,
9,
10,
Upper
Quartile
= 10
Max
10,
15
Highest
= 15
Drawing Box and Whisker
Diagrams.
Step 3: Draw a Box plot
3,
4,
Lowest
= 3
3
4,
6,
8,
Lower
Quartile
= 4
4
5
Q3
Q2
Q1
Min
8,
8,
7
8
9
10,
10,
Upper
Quartile
= 10
Median
= 8
6
9,
Max
10 11
12 13
15
Highest
= 15
14 15
Your Turn:
Draw box and whisker plots for the following
Lowest
Lower
Quartile
Median
Upper
Quartile
Highest
Question
2 14
17
A
3
7
24
34
42
B
1
5
10
43
70
C
4
9
17
26
30
D
13
23
62
83
87
E
2
4
9
17
31
F
1
2
4
5
8
G
1
7
9.5
22
35
H
2
7
13
18
20
I
18
32
39
45
50
Answers:
A
0
B0
C
0
5
10
15
20
25
30
35
10
20
30
40
50
60
70
5
10
15
20
25
30
40
45
Answers:
D 10
E
F
0
1
20
30
40
50
60
70
80
5
10
15
20
25
30
35
3
4
5
6
7
8
2
90
Answers:
G
0
5
10
15
20
25
H0
4
8
12
16
20
I
15
20
25
30
35
40
30
35
45
50
Extension: Box and whisker plots:
For the dot plot below draw a box and whisker graph
List the data in order:
24
18 19 19 19 21 21 22 23 23 23 24 24 24 24 24 25 25 26 26 26 28 28
Find the 5 data points
Draw the box and whisker graph
18
20
22
24
26
28
Web resources:
http://www.youtube.com/watch?v=GMb6HaLXmjY
(you tube video explanation of how to draw a box and whisker plot)
http://www.brainingcamp.com/resources/math/box-plots/lesson.php
(Good interactive notes for teaching box and whisker, but a little long)
http://www.brainingcamp.com/resources/math/box-plots/interactive.php
(interactive box and whisker, could be good for teaching)
Thanks
This power point has been put together
using power points, images, videos and
games from the net.
Thank you to all those who have placed
their work in the public domain. For others
to use.