Statistics: The branch of mathematics
that deals with collecting, organizing,
and analyzing or interpreting data.
Data: Numerical facts or numerical
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 placevalue position are then used to form the
leaves.
Leaf: The last digit on the right of the
number.
Stem: The digit or digits that remain when
the leaf is dropped.
Look at the number 284
The leaf is the last digit formed: the number 4.
The stem is the remaining digits when the leaf is dropped: the number 28.
The stem with the leaf forms the number 284.
Stem
28
4
Leaf
= 284
Here are the scores from two periods of math
class. Students took the same test.
Period 1: 77 79 85 58 97 94 82 81 75 63 60 92 75
98 83 58 72 57 70 81
Period 2: 57 60 88 85 79 70 65 98 97 59 58 65 62
77 77 75 73 69 82 81
Period 1: 76 79 85 58 97 94 82 81 75 63 60 92
75 98 83 58 72 57 70 81 Notice that the data (numerical facts)
A key
should be
included
when
making a
stemand-leaf
plot.
Stem
5
Leaf
8 8 7
are numbers between 57-98. Create the
stem by listing numbers from 5-9.
Stem
Leaf
6
3 0
5
7 7 8
7
6 9 5 5 2 0
6
0 3
7
0 2 5 5 6 9
8
1 1 2 3 5
9
2 4 7 8
8
5 2 1 3 1
9
7 4 2 8
Key: 7 9 means 79
Rearrange
the leaf in
numerical
order from
least to
greatest
Match up the data to the stem-and-leaf. The last digit in 76 will match up with the stem 7.
Then the last digit in 79 will match up with the stem 7. Then the last digit in 85 will match
up with the stem 8 and this pattern will continue until all data have been recorded in the
Period 2: 57 60 88 85 79 70 65 98 97 59 58 65
Notice that the data (numerical facts)
62 77 77 75 73 69 82 81
Stem
are numbers between 57-98. Create the
stem by listing numbers from 5-9.
Leaf
5
7 9 8
6
0 5 5 2 9
9 0 7 7 5 3
7
8
9
8 5 2 1
8 7
Key: 7
Stem
5
9 means 79
Rearrange the leaf
in numerical order
from least to
greatest
Leaf
7 8 9
6
0 2 5 5 9
7
0 3 5 7 7 9
8
9
1 2 5 8
7 8
Match up the data to the stem-and-leaf. The last digit in 57 will match up with the stem 5.
Then the last digit in 60 will match up with the stem 6. Then the last digit in 88 will match
up with the stem 8 and this pattern will continue until all data have been recorded in the
stem-and-leaf.
Now compare the data from the two periods.
Period 1: 77 79 85 58 97 94 82 81 75 63 60 92 75
98 83 58 72 57 70 81
Period 2: 57 60 88 85 79 70 65 98 97 59 58 65 62
77 77 75 73 69 82 81
Stem
Leaf - period 2
Stem
Leaf - period 1
5
7 8 9
5
7 7 8
0 2 5 5 9
Key: 7 9 means 79
6
6
0 3
0 3 5 7 7 9
7
7
0 2 5 5 6 9
8
1 2 5 8
8
1 1 2 3 5
7 8
9
2 4 7 8
9
The data from the two classes indicates that the
test given appears to be valid. Both classes are
very similar in test scores. Overall period 1 scored
better.
Stem
5
6
7
Leaf - period 1
7 7 8
0 3
Key: 7 9 means 79
0 2 5 5 6 9
8
1 1 2 3 5
9
2 4 7 8
Stem
Leaf - period 2
5
7 8 9
0 2 5 5 9
6
7
0 3 5 7 7 9
8
1 2 5 8
7 8
9
Additional numerical facts indicate that the lowest
grade in both classes was a 57 and the highest
score was a 98 in both classes. The median score
for the 20 test scores from period 1 is between a
76 and 79. And the median test score for period 2
is between a 73 and 75.
Stem
Leaf - period 2
Stem
Leaf - period 1
5
7 8 9
5
7 7 8
0 2 5 5 9
6
6
0 3 Key: 7 9 means 79
0 3 5 7 7 9
7
7
0 2 5 5 6 9
8
1 2 5 8
8
1 1 2 3 5
7 8
9
2 4 7 8
9
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
Notice that the data (numerical facts) are numbers between 4269. Create the stem by listing numbers from 4-6.
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
Key: 5 7 means 57
Match up the data to the stem-and-leaf. The last digit in 57 will match up with the stem 5.
Then the last digit in 61 will match up with the stem 6. Then the last digit in 57 will match
up with the stem 5 and this pattern will continue until all data have been recorded in the
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
Key: 5 7 means 57
It is easy to interpret or analyze information from the Stemand-Leaf.
1. How many presidents were 51 years old at their
inauguration? 23
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)
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
Key: 5 7 means 57