How to Draw Stem Plots, How to read them, ansd how to find the Median from them. Includes Groups of Five S&L Plots. For information about obtaining a PowerPoint format download of this presentation, go to the following page: http://passyworldofmathematics.com/pwerpoints/

1. Stem and Leaf Plots
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
Camera and Battery Images from Google Images

2. 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

3. 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.

4. Frequency Table for Battery Life
Battery Life FREQUENCY Actual Values
Here is the Frequency
0-9 4 4, 5, 5, 7
Table for our camera
10-19 5 10, 14, 15,
15, 17 battery test results:
20-29 5 20, 22, 23,
26, 27
30-39 3 32, 34, 36 26, 32, 14, 10, 5, 34,
40-49 0 4, 7, 15, 17, 15, 22,
50-59 1 56
27, 20, 23, 36, 5,
60-69 0
56, 75
70-79 1 75

5. 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”.)

6. Stem and Leaf Diagram to show camera
battery life under various conditions
Key : 5 | 6 = 56 hours
Battery Life Actual Values STEM LEAF
0-9 4, 5, 5, 7 Ones 0 4 5 5 7
10-19 10, 14, 15, 15, 17 Tens 1 0 4 5 5 7
20-29 20, 22, 23, 26, 27 Twenties 2 0 2 3 6 7
30-39 32, 34, 36 Thirties 3 2 4 6
40-49 Fourties 4
50-59 56 Fifties 5 6
60-69 Sixties 6
70-79 75 Seventies 7 5

7. The Structure and Values for a
Stem and Leaf Diagram
In a Stem and Leaf
Plot, the data
values are put in Key : 5 | 6 = 56 hours
order from the
Lowest to Highest.
Battery Life Data Values STEM LEAF
We then group
0-9
them into : 4, 5, 5, 7 Ones 0 4 5 5 7
10-19 10, 14, 15, 15, 17 Tens 1 0 4 5 5 7
Ones = 0 to 9
20-29
Tens = 10 to 19 20, 22, 23, 26, 27 Twenties 2 0 2 3 6 7
and so on. These 3 2 4 6
30-39 32, 34, 36 Thirties
groups are called
the40-49
“Stems”. Fourties 4
50-59 56 Fifties 5 6
The “Leaf” is the
60-69
last digit on each Sixties 6
of the original 7 5
70-79 75 Seventies
data values.

8. 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

9. 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
A Stem and Leaf Plot puts all of the
data values into order, and places
4 them in groups. It also has the same
5 6 shape as a Bar Chart of the data.
6
7 5
It is like a Bar Chart, but with the
data values written onto it, instead
of having coloured bars.

10. Reading Stem and Leaf Plots
STEM LEAF
0 4 5 5 7 Ones 0|5 = 5
1 0 4 5 5 7
2 0 2 3 6 7 Twenties
2|6 = 26 (Not 6)
3 2 4 6
4
5 6 Fifties 5|6 = 56 (Not 6)
6
7 5
Key : 5 | 6 = 56 hours

11. Stem and Leaf – Maximum and Minimum
The Minimum value is always
STEM LEAF at the start of the S&L Plot:
0 4 5 5 7 0|4 = 4
1 0 4 5 5 7
The Maximum value is
2 0 2 3 6 7 always at the end of the S&L
3 2 4 6 plot: 7|5 = 75
4
5 6 The S&L contains 19 values,
(not 27 values).
6
7 5 Eg. Only count how many
Leaves there are.
Key : 5 | 6 = 56 hours

12. Stem and Leaf – Median Average
STEM LEAF Because the data values
0 4 5 5 7 are in order, (from lowest
1 0 4 5 5 7 to highest), we can easily
2 0 2 3 6 7 find the middle “Median”
3 2 4 6 by crossing off values from
4 each end, until we reach
5 6 the middle value.
6
7 5
Median = 20 hours
Key : 5 | 6 = 56 hours

13. Stem and Leaf – Double Medians
For our Camera Battery Life
STEM LEAF results, we had 19 results
contained in the leaves.
0 4 5 5 7
1 0 4 5 5 7 Whenever we have an ODD
number of items like this, there
2 0 2 3 6 7 is always only one middle
3 2 4 6 number which is the “Median”.
4 The next example shows an
5 6 EVEN number of items.
6 For an EVEN number of
7 5 items, we will always have two
middle numbers.
Key : 5 | 6 = 56 hours

14. Stem and Leaf – Double Medians
Here is a different set of Battery
STEM LEAF Life results, where we have 22
0 4 5 5 7
results contained in the leaves.
1 0 4 5 5 7 Whenever we have an EVEN
2 0 2 3 6 7 number of items like this, there
3 2 4 6 are always two middle numbers.
4
We find the midpoint of these
5 6 6 9 two numbers by adding them
6 together and dividing by 2.
7 5 8
Median = ( 22 + 23 ) / 2
Key : 5 | 6 = 56 hours Median = 22.5 hours.

15. 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 5, 4, 7, 5
Tens 14, 10, 15, 17, 15
Twenties 26, 22, 27, 20, 23 Next we need to set up
Thirties 32, 34, 36 stems for the ones
Fifties 56 through to the seventies.
Seventies 75 (See next slide)

16. Making a Stem and Leaf Plot
Ones 5, 4, 7, 5 STEM LEAF
Tens 14, 10, 15, 17, 15 0
1
Twenties 26, 22, 27, 20, 23
2
Thirties 32, 34, 36 3
Fourties 4
5
Fifties 56
6
Sixties
7
Seventies 75
Next we need to set up Leaves for all of the original values. (See next slide)

17. Making a Stem and Leaf Plot
Ones 5, 4, 7, 5 STEM LEAF
Tens 14, 10, 15, 17, 15 0 5 4 7 5
1 4 0 5 7 5
Twenties 26, 22, 27, 20, 23
2 6 2 7 0 3
Thirties 32, 34, 36 3 2 4 6
Fourties 4
5 6
Fifties 56
6
Sixties
7 5
Seventies 75
We only take the last digit of each data value when making the leaves.

18. Unordered Stem and Leaf Plot
STEM LEAF
Our Stem and Leaf Plot
0 5 4 7 5 does not have our data
1 4 0 5 7 5 placed into order from
2 6 2 7 0 3 lowest to highest.
3 2 4 6
4
5 6
We call this plot an
6 “Unordered Stem and
7 5 Leaf Plot”.
Key : 5 | 6 = 56 hours

19. 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 Place 2 0 2 3 6 7
3 2 4 6 the 3 2 4 6
4
leaves 4
into
5 6 5 6
order
6 6
7 5 7 5
Key : 5 | 6 = 56 hours Key : 5 | 6 = 56 hours
Unordered Stem and Leaf Plot Ordered Stem and Leaf Plot

20. Groups of Five S&L Plot
Groups of Five
Stem and Leaf STEM LEAF
Plot 0 4
0* 5 5 7
Groups of Ten S&L Plot 1 0 4
1* 5 5 7
STEM LEAF 2 0 2 3
0 4 5 5 7 Split 2* 6 7
1 0 4 5 5 7 each 3 2 4
2 0 2 3 6 7 group 3* 6
3 2 4 6
of ten 4
4
in half 5
5 6 5* 6
6 6
7 5 7
7* 5

21. Groups of Five S&L Plot
Groups of Five
Stem and Leaf STEM LEAF
Plot 0 4
0 to 4
* 5 to 9 0* 5 5 7
In a Groups of Five S&L 10 to 14 1 0 4
Plot, the groups each
* 15 to 19 1* 5 5 7
contain a range of five.
20 to 24 2 0 2 3
0 to 4 = 0,1,2,3,4 = five * 25 to 29 2* 6 7
items (count them on 30 to 34 3 2 4
your fingers).
* 35 to 39 3* 6
The tens, for example 40 to 44 4
have a lower range of * 45 to 49 4*
10 to 14 named as 1 | 50 to 54 5
and * 55 to 59 5*
an upper range of
15 to 19 named as 1* | etc

22. 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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