The document describes how to create a back-to-back stem and leaf plot to compare the battery life data from two phone brands. It shows the raw battery life data for each brand in hours. Then it draws individual stem and leaf plots for each brand's data. Finally, it combines the two plots by reversing one and placing them side by side to allow direct comparison of the battery life distributions between the two brands.

1. STEM LEAF
0 7
1 0 5 7 7 9
2 0 2 3 6 7
3 2 4 6 8
4 3
5 6
6
7 1
Key : 5 | 6 = 56 hours
Back to Back Stem & Leaf Diagrams

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
6
7 5
Key : 5 | 6 = 56 hours
Notice how the Bar Chart and the S&L
Diagram have the same overall shape.
Bar Chart and Stem & Leaf Diagram for
Camera Battery Life Testing

3. Two Mobile Phones have been tested for Battery
Life in between charges. We need to create a
Back to Back Stem and Leaf Plot to show the
comparison of the battery life results.
It is assumed that people already know how to
do basic Stem and Leaf Plots.
The raw data is shown on the next slide
Back to Back Stem & Leaf Diagrams

4. “Phone Brand A” – 7, 10, 15, 15, 17, 17, 19, 20,
22, 22, 26, 27, 30, 32, 34, 36, 38, 56, 75 (hours)
“Phone Brand B” – 5, 7, 8, 8, 10, 11, 14, 17, 19,
21, 22, 22, 22, 30, 32, 34, 36, 38, 61 (hours)
The next step is to group this data into ones, tens,
twenties, thirties, … and so on. (See Next Slide).
Battery Life Test Results

5. We will now draw an S&L Plot for “Brand A”
Brand “A”
7
10, 15, 15, 17, 17, 19
20, 22, 22, 26, 27
30, 32, 34, 36, 38
56,
75
Battery Life Test Results
Brand B”
5, 7, 8, 8
10, 11, 14, 17, 19
21, 22, 22, 22
30, 32, 34, 36, 38
61

6. STEM LEAF
0 7
1 0 5 5 7 7 9
2 0 2 2 6 7
3 0 2 4 6 8
4
5 6
6
7 5
Key : 5 | 6 = 56 hours
Stem and Leaf Diagram to show “Brand A”
battery life under various conditions
Hours Actual Values
0-9 7
10-19 10, 15, 15, 15, 17, 19
20-29 20, 22, 22, 26, 27
30-39 30, 32, 34, 36, 38
40-49
50-59 56
60-69
70-79 75
Ones
Tens
Twenties
Thirties
Fourties
Fifties
Sixties
Seventies

7. STEM LEAF
0 7
1 0 5 5 5 7 9
2 0 2 2 6 7
3 0 2 4 6 8
4
5 6
6
7 5
Key : 5 | 6 = 56 hours
The Structure and Values for Brand A
Stem and Leaf Diagram
Battery Life Data Values
0-9 7
10-19 10, 15, 15, 15, 17,19
20-29 20, 22, 22, 26, 27
30-39 30, 32, 36, 38
40-49
50-59 56
60-69
70-79 75
Ones
Tens
Twenties
Thirties
Fourties
Fifties
Sixties
Seventies
In a Stem and
Leaf Plot, the
data values are
put in order
from the Lowest
to Highest.
We then group
them into :
Ones = 0 to 9
Tens = 10 to 19
and so on.
These groups are
called the
“Stems”.
The “Leaf” is the
last digit on each
of the original
data values.

8. STEM LEAF
0 5 7 8 8
1 0 1 4 7 9
2 1 2 2 2
3 0 2 4 6 8
4
5
6 1
7
Key : 6 | 1 = 61 hours
Stem and Leaf Diagram to show “Brand B”
battery life under various conditions
Hours Actual Values
0-9 5, 7, 8, 8
10-19 10, 11, 14, 17, 19
20-29 21, 22, 22, 22
30-39 30, 32, 34, 36, 38
40-49
50-59
60-69 1
70-79
Ones
Tens
Twenties
Thirties
Fourties
Fifties
Sixties
Seventies

9. STEM LEAF
0 7
1 0 5 5 5 7 9
2 0 2 2 6 7
3 0 2 4 6 8
4
5 6
6
7 5
Brand A and B Stem & Leaf Plots
STEM LEAF
0 5 7 8 8
1 0 1 4 7 9
2 1 2 2 2
3 0 2 4 6 8
4
5
6 1
7
We now make the “Back to Back” Stem and Leaf Diagram by
flipping the Red Brand B Diagram around the other way, and
merging it with the Blue Brand A Diagram so that they share
the same stems down the middle.

10. Creating the Back to Back S&L Plot involves
reversing our first S&L, like reversing a person.
Making a BACK TO BACK Stem & Leaf Plot
Images Source: Google Images

11. REVERSING the Brand B Leaf Plot
STEM LEAF
0 5 7 8 8
1 0 1 4 7 9
2 1 2 2 2
3 0 2 4 6 8
4
5
6 1
7
To swap around the Brand B S&L Plot, we make the leaves
go out to the left, instead of to the right.
It is like reflecting our original in a mirror.
LEAF STEM
8 8 7 5 0
9 7 4 1 0 1
2 2 2 1 2
8 6 4 2 0 3
4
5
1 6
7

12. STEM LEAF
0 7
1 0 5 5 5 7 9
2 0 2 2 6 7
3 0 2 4 6 8
4
5 6
6
7 5
Brand A and B Stem & Leaf Plots
We now combine the reversed around red “Brand B” S&L
Plot, with our blue “Brand A” S&L Plot, to make a single
combined “Back to Back” S&L Plot as shown on next slide.
LEAF STEM
8 8 7 5 0
9 7 4 1 0 1
2 2 2 1 2
8 6 4 2 0 3
4
5
1 6
7

13. “Brand B” LEAF STEM LEAF “Brand A”
8 8 7 5 0 7
9 7 4 1 0 1 0 5 5 5 7 9 Key: 6|1 =
2 2 2 1 2 0 2 2 6 7 61 hours
8 6 4 2 0 3 0 2 4 6 8
4
5 6
1 6
7 5
We made this “Back to Back” Stem and Leaf Diagram by
flipping the Red Brand B Diagram around the other way,
and merging it with the Blue Brand A Diagram, to that they
now share the same set of stems down the middle.
Making the BACK TO BACK Stem & Leaf Plot
Conclusion:
The Battery
Life is about
the same.

14. Phone Battery Comparison
“Brand A” “Brand B”
LEAF STEM LEAF
8 8 7 5 0 7
9 7 4 1 0 1 0 5 5 5 7 9
2 2 2 1 2 0 2 2 6 7
8 6 4 2 0 3 0 2 4 6 8
4
5 6
1 6
7 5
Key : 6 | 1 = 61 hours

15. http://passyworldofmathematics.com/