Stem and Leaf Plots
Key : 5 | 6 = 56 hours
STEM
0
1
2
3
4
5
6
7
LEAF
4 5 5 7
0 4 5 5 7
0 2 3 6 7
2 4 6
6
5
Camera and Battery Images from Google Images
Camera Battery Life Testing
A magazine did some testing to see how long camera
batteries lasted before they needed recharging.
(Several cameras and test conditions were used).
The results, measured in number of hours until a
camera’s battery was flat, were as follows:
26, 32, 14, 10, 5, 34, 4, 7, 15, 17, 15,
22, 27, 20, 23, 36, 5, 56, 75
Organising Battery Life Test Results
Our first step in analysing this data is to construct a Frequency
Table of the results.
26, 32, 14, 10, 5, 34, 4, 7, 15, 17, 15, 22, 27, 20, 23, 36, 5, 56, 75
The Highest value is 75, and the lowest value is 4.
This gives a Range of 75 - 4 = 71.
Size of Class Intervals = Range / 10 = 71 divided by 10 = 7.1 = 7
Seven is not the easiest of numbers to work with, and so we have
decided to group our data into Groups of 10.
Frequency Table for Battery Life
Battery Life
FREQUENCY Actual Values
0-9
4
4, 5, 5, 7
10-19
5
10, 14, 15,
15, 17
20-29
5
20, 22, 23,
26, 27
30-39
3
32, 34, 36
40-49
0
50-59
1
60-69
0
70-79
1
56
75
Here is the Frequency
Table for our camera
battery test results:
26, 32, 14, 10, 5, 34,
4, 7, 15, 17, 15, 22,
27, 20, 23, 36, 5,
56, 75
Bar Graph for Battery Life
Battery Life
FREQUENCY
0-9
4
10-19
5
20-29
5
30-39
3
40-49
0
50-59
1
60-69
0
70-79
1
(The Horizontal Bar Chart for our
results, made using “Chart Go”.)
Stem and Leaf Diagram to show camera
battery life under various conditions
Key : 5 | 6 = 56 hours
Battery Life
Actual Values
0-9
4, 5, 5, 7
10-19
10, 14, 15, 15, 17
20-29
20, 22, 23, 26, 27
30-39
32, 34, 36
40-49
50-59
56
60-69
70-79
75
STEM LEAF
Ones
0
4 5 5 7
Tens
1
0 4 5 5 7
Twenties
2
0 2 3 6 7
3
2 4 6
Thirties
Fourties
4
Fifties
5
Sixties
6
Seventies
7
6
5
In a Stem and Leaf
Plot, the data
values are put in
order from the
Lowest to Highest.
Battery Life
Data Values
We then group
0-9into :
4, 5, 5, 7
them
10-19
Ones = 0 to 9
20-29
Tens
= 10 to 19
and so on. These
30-39
groups are called
the40-49
“Stems”.
50-59
The “Leaf” is the
last60-69
digit on each
of the original
70-79
data values.
The Structure and Values for a
Stem and Leaf Diagram
Key : 5 | 6 = 56 hours
STEM LEAF
Ones
0
4 5 5 7
10, 14, 15, 15, 17
Tens
1
0 4 5 5 7
20, 22, 23, 26, 27
Twenties
2
0 2 3 6 7
3
2 4 6
32, 34, 36
56
75
Thirties
Fourties
4
Fifties
5
Sixties
6
Seventies
7
6
5
Bar Chart and Stem & Leaf Diagram for
Camera Battery Life Testing
Notice how the Bar Chart and the S&L
Diagram have the same overall shape.
Key : 5 | 6 = 56 hours
STEM LEAF
0
4 5 5 7
1
0 4 5 5 7
2
0 2 3 6 7
3
2 4 6
4
5
6
6
7
5
Stem and Leaf Plot Values and Shape
Key : 5 | 6 = 56 hours
STEM LEAF
0
4 5 5 7
1
0 4 5 5 7
2
0 2 3 6 7
3
2 4 6
4
5
6
6
7
5
A Stem and Leaf Plot puts all of the
data values into order, and places
them in groups. It also has the same
shape as a Bar Chart of the data.
It is like a Bar Chart, but with the
data values written onto it, instead
of having coloured bars.
Reading Stem and Leaf Plots
STEM
0
1
2
3
4
LEAF
4 5 5 7
0 4 5 5 7
0 2 3 6 7
2 4 6
5
6
6
7
5
Key : 5 | 6 = 56 hours
Ones
0|5 = 5
Twenties
2|6 = 26 (Not 6)
Fifties
5|6 = 56 (Not 6)
Stem and Leaf – Maximum and Minimum
STEM
0
1
2
3
4
LEAF
4 5 5 7
0 4 5 5 7
0 2 3 6 7
2 4 6
The Minimum value is always
at the start of the S&L Plot:
0|4 = 4
The Maximum value is
always at the end of the S&L
plot: 7|5 = 75
5
6
6
7
The S&L contains 19 values,
(not 27 values).
5
Eg. Only count how many
Leaves there are.
Key : 5 | 6 = 56 hours
Stem and Leaf – Median Average
STEM
0
1
2
3
4
LEAF
4 5 5 7
0 4 5 5 7
0 2 3 6 7
2 4 6
5
6
6
7
5
Key : 5 | 6 = 56 hours
Because the data values
are in order, (from lowest
to highest), we can easily
find the middle “Median”
by crossing off values from
each end, until we reach
the middle value.
Median = 20 hours
Stem and Leaf – Double Medians
STEM
0
1
2
3
4
5
6
7
LEAF
4 5 5 7
0 4 5 5 7
0 2 3 6 7
2 4 6
6
5
Key : 5 | 6 = 56 hours
For our Camera Battery Life
results, we had 19 results
contained in the leaves.
Whenever we have an ODD
number of items like this, there
is always only one middle
number which is the “Median”.
The next example shows an
EVEN number of items.
For an EVEN number of items,
we will always have two middle
numbers.
Stem and Leaf – Double Medians
STEM
0
1
2
3
4
LEAF
4 5 5 7
0 4 5 5 7
0 2 3 6 7
2 4 6
5
6 6 9
6
7
5 8
Key : 5 | 6 = 56 hours
Here is a different set of Battery
Life results, where we have 22
results contained in the leaves.
Whenever we have an EVEN
number of items like this, there
are always two middle numbers.
We find the midpoint of these
two numbers by adding them
together and dividing by 2.
Median = ( 22 + 23 ) / 2
Median = 22.5 hours.
Making a Stem and Leaf Plot
Our original Battery Testing results were as follows:
26, 32, 14, 10, 5, 34, 4, 7, 15, 17, 15, 22, 27, 20, 23, 36, 5, 56, 75
We need to separate out these results into Groups of 10.
Ones
Tens
Twenties
Thirties
Fifties
Seventies
5, 4, 7, 5
14, 10, 15, 17, 15
26, 22, 27, 20, 23
32, 34, 36
56
75
Next we need to set up
stems for the ones
through to the seventies.
(See next slide)
Making a Stem and Leaf Plot
Ones 5, 4, 7, 5
Tens 14, 10, 15, 17, 15
Twenties 26, 22, 27, 20, 23
Thirties 32, 34, 36
Fourties
Fifties 56
Sixties
Seventies 75
STEM LEAF
0
1
2
3
4
5
6
7
Next we need to set up Leaves for all of the original values. (See next slide)
Making a Stem and Leaf Plot
Ones 5, 4, 7, 5
Tens 14, 10, 15, 17, 15
Twenties 26, 22, 27, 20, 23
Thirties 32, 34, 36
Fourties
Fifties 56
Sixties
Seventies 75
STEM LEAF
0
5 4 7 5
1
4 0 5 7 5
2
6 2 7 0 3
3
2 4 6
4
5
6
6
7
5
We only take the last digit of each data value when making the leaves.
Unordered Stem and Leaf Plot
STEM LEAF
0
5 4 7 5
1
4 0 5 7 5
2
6 2 7 0 3
3
2 4 6
4
5
6
6
7
5
Key : 5 | 6 = 56 hours
Our Stem and Leaf Plot
does not have our data
placed into order from
lowest to highest.
We call this plot an
“Unordered Stem and
Leaf Plot”.
Ordered Stem and Leaf Plot
STEM LEAF
STEM LEAF
0
5 4 7 5
0
4 5 5 7
1
4 0 5 7 5
1
0 4 5 5 7
2
6 2 7 0 3
2
0 2 3 6 7
3
2 4 6
3
2 4 6
4
5
6
6
7
5
Place
the
leaves
into
order
4
5
6
6
7
5
Key : 5 | 6 = 56 hours
Key : 5 | 6 = 56 hours
Unordered Stem and Leaf Plot
Ordered Stem and Leaf Plot
Groups of Five S&L Plot
Groups of Five
Stem and Leaf
Plot
STEM LEAF
0
4
0* 5 5 7
Groups of Ten S&L Plot
1
0 4
1* 5 5 7
2
STEM LEAF
0
4 5 5 7
1
0 4 5 5 7
2
0 2 3 6 7
3
2 4 6
4
5
6
2* 6 7
3
2 4
3* 6
4
5
5* 6
6
6
7
Split
each
group
of ten
in half
0 2 3
5
7
7*
5
Groups of Five
Stem and Leaf
Plot
Groups of Five S&L Plot
STEM LEAF
0 to 4
* 5 to 9
In a Groups of Five S&L
Plot, the groups each
contain a range of five.
0 to 4 = 0,1,2,3,4 = five
items (count them on
your fingers).
The tens, for example
have a lower range of
10 to 14 named as 1 |
and
an upper range of
15 to 19 named as 1* |
10 to 14
* 15 to 19
20 to 24
* 25 to 29
30 to 34
* 35 to 39
40 to 44
* 45 to 49
50 to 54
* 55 to 59
0
4
0* 5 5 7
1
0 4
1* 5 5 7
2
0 2 3
2* 6 7
3
2 4
3* 6
4
4*
5
5*
etc
Stem and Leaf Plot - SUMMARY
• Stem and Leaf Plots have data placed into
order from lowest to highest.
• They consist of a Stem Column (in tens)
and a Leaf Column that has last digits only
• Because the data is in order, we can cross off
forward and backward and find the Median
• The shape of the S&L Plot is the same as a
horizontal Bar Chart of the data.
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