Displaying & Analyzing Data
Stem-and-leaf Plot
Box-and-Whisker Plot
Venn Diagrams
Statistics: The branch of mathematics
that deals with collecting, organizing,
analyzing or interpreting data.
Data: Numerical facts or information.
Stem-and-Leaf Plots: A convenient
method to display every piece of data
by showing the digits of each number.
In a stem-and-leaf plot, the
greatest common place value of
the data is used to form stems.
The numbers in the next
greatest place value position
are then used to form the
leaves.
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)
Stem
4
Leaf
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 1 9 4
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)
Stem Leaf
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
It is easy to interpret or analyze information from the Stemand-Leaf.
1. How many presidents were 51 years old at their
inauguration? 4
2. What age is the youngest president to be inaugurated? 42
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
Stem Leaf: Age of United States Presidents at their First Inauguration
(through the 40th Presidency)
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
Data Displays
A box-and-whisker plot shows
how data is distributed by using
the median, upper and lower
quartiles, and the greatest and
least values in the data set.
17, 18, 19, 21, 24,26, 27
The lower quartile (LQ) is the median of
the lower half of the data.
The LQ is 18.
The upper quartile (UQ) is the
median of the upper half of the data.
The UQ is 26.
___
__
16 17 18 19 20 21 22 23 24 25 26 27 28
Make a Box & Whisker Plot
76, 78, 82, 87, 88, 88, 89, 90, 91, 95
88
Find the median of this
segment (LQ)
LQ = 82
Find the median of
this segment.
UQ = 90
Lower
Quartile
(LQ)
Least
Value
76,
65
78,
70
82,
75
Middle
Quartile
87,
88,
80
88,
85
Upper
Quartile
89,
90,
90
91,
95
Now for the box and whisker
Greatest
Value
95
100 105
Lower
Quartile
(LQ)
Least
Value
76,
65
78,
70
82,
75
Middle
Quartile
87,
88,
80
88,
85
Upper
Quartile
89,
90,
90
Greatest
Value
91,
95
95
100 105
What number represents 25% of the data?
LQ 82
What number represents 50% of the data?
Median 88
What number represents 75% of the data?
UQ 90
Venn Diagrams
Content Standard:
Begin to identify information in a Venn
diagram
Click for
the next
screen.
The diagram shows the results of your
survey on ice cream preferences for 23
friends.
How many of your friends liked
chocolate and/or vanilla ice cream?
How many students are not
in the diagram? Why?
13
1
8
Click for
an answer.
How many students are not
in the diagram? Why?
23
One student is not in
the diagram. He must
not like chocolate or
vanilla ice cream.
-22
1
13
1
8
The
End.
Stem and Leaf Plot
Stem and leaf plots are used as a quick
way of seeing how many pieces of data
fall in various ranges. The reader can
quickly tell:
- the range
- the mode
Stem and leaf plots have a title, a stem,
and leaves
A key is used to explain how to read the
stem and leaves.
Box - and - Whisker Plot
Displays large set of
data.
Gives general idea
of how data
clusters.
Graph includes:
- Title
- Labeled intervals
- Box between
lower and upper
quartiles
- Whiskers from
quartiles to
extremes
- Median, quartiles
and whiskers labeled
Displaying & Analyzing Data
Stem-and-leaf Plot
Box-and-Whisker Plot
Venn Diagrams