Statistics: Stem-and-Leaf Plots

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Statistics Stem-and-Leaf Plots
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Statistics Stem-and-Leaf Plots

• 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.

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Statistics Stem-and-Leaf Plots

• 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.

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Statistics Stem-and-Leaf Plots

• 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
Leaf
28
4
284
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Statistics Stem-and-Leaf Plots
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
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Statistics Stem-and-Leaf Plots
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) are
numbers between 57-98. Create the stem by listing
numbers from 5-9.
Stem
Leaf
5 6 7 8 9
8
8
7
Stem
Leaf
A key should be included when making a
stem-and-leaf plot.
3
0
5 6 7 8 9
7 7 8
6
9
5
5
2
0
0 3
Rearrange the leaf in numerical order from least
to greatest
5
2
1
3
1
0 2 5 5 6 9
7
4
2
8
1 1 2 3 5
Key 7 9 means 79
2 4 7 8
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 stem-and-leaf.
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Statistics Stem-and-Leaf Plots
Period 2 57 60 88 85 79 70 65 98 97 59 58 65 62
77 77 75 73 69 82 81
Notice that the data (numerical facts) are
numbers between 57-98. Create the stem by listing
numbers from 5-9.
Stem
Leaf
Stem
Leaf
5 6 7 8 9
5 6 7 8 9
7
9
8
7 8 9
Key 7 9 means 79
0
5
9
2
5
0 2 5 5 9
9
0
7
7
3
5
0 3 5 7 7 9
Rearrange the leaf in numerical order from least
to greatest
8
5
2
1
1 2 5 8
8
7
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.
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Statistics Stem-and-Leaf Plots
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
7 8 9
5 6 7 8 9
5 6 7 8 9
7 7 8
0 2 5 5 9
Key 7 9 means 79
0 3
0 3 5 7 7 9
0 2 5 5 6 9
1 2 5 8
1 1 2 3 5
7 8
2 4 7 8
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Statistics Stem-and-Leaf Plots
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
Leaf - period 2
Stem
Leaf - period 1
7 8 9
5 6 7 8 9
5 6 7 8 9
7 7 8
0 2 5 5 9
0 3
Key 7 9 means 79
0 3 5 7 7 9
0 2 5 5 6 9
1 2 5 8
1 1 2 3 5
7 8
2 4 7 8
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Statistics Stem-and-Leaf Plots
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
7 8 9
5 6 7 8 9
5 6 7 8 9
7 7 8
0 2 5 5 9
0 3
Key 7 9 means 79
0 3 5 7 7 9
0 2 5 5 6 9
1 2 5 8
1 1 2 3 5
7 8
2 4 7 8
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Statistics Stem-and-Leaf Plots
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)
Notice that the data (numerical facts) are
numbers between 42-69. Create the stem by listing
numbers from 4-6.
Stem
Leaf
9
9
6
8
7
2
3
4 5 6
0
7
7
7
7
1
6
8
4
4
2
0
4
5
1
6
1
5
4
1
5
6
2
Key 5 7 means 57
1
8
4
1
5
0
2
1
9
4
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 stem-and-leaf.
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Statistics Stem-and-Leaf Plots
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)
Rearrange the leaf in numerical order from least
to greatest
Stem
Leaf
4 5 6
2 3 6 7 8 9 9
Key 5 7 means 57
0 0 1 1 1 1 2 2 4 4 4 4 5 5 5 6 6
6 7 7 7 7 8
0 1 1 1 2 4 4 5 8 9
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Statistics Stem-and-Leaf Plots

• It is easy to interpret or analyze information
  from the Stem-and-Leaf.
• How many presidents were 51 years old at their
  inauguration?
• What age is the youngest president to be
  inaugurated?
• What is the age of the oldest president to be
  inaugurated?
• How many presidents were 40-49 years old at their
  inauguration?

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42
69
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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 5 6
2 3 6 7 8 9 9
0 0 1 1 1 1 2 2 4 4 4 4 5 5 5 6 6
6 7 7 7 7 8
Key 5 7 means 57
0 1 1 1 2 4 4 5 8 9