Statistics: Stem-and-Leaf Plots

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Statistics: Stem-and-Leaf Plots. Week of 4/11/11 Day 3. 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.

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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.

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.

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

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

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: 79 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.

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: 79 means 79

0

5

5

2

9

0 2 5 5 9

9

0

7

7

5

3

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.

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

5

6

7

8

9

7 8 9

5

6

7

8

9

7 7 8

0 2 5 5 9

Key: 79 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

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

5

6

7

8

9

7 8 9

5

6

7

8

9

7 7 8

0 2 5 5 9

0 3

Key: 79 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

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

5

6

7

8

9

7 8 9

5

6

7

8

9

7 7 8

0 2 5 5 9

0 3

Key: 79 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

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

8

6

9

7

2

3

4

5

6

7

7

7

8

7

4

1

0

2

6

4

0

5

4

1

6

5

1

4

1

5

6

2

Key: 57 means 57

1

1

8

4

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.

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: 57 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

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?

4

42

69

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

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: 57 means 57

0 1 1 1 2 4 4 5 8 9

Statistics: Back to Back 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.

Back to Back Stem-and-Leaf Plots: Used to compare two sets of data. The leaves for one set of data are on one side of the stem, and the leaves for the other set of data are on the other side.

Leaf

Stem

Leaf

7

28

4

= 284

= 287

Statistics: Back to Back 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

Create a Back to Back Stem-and-Leaf plot for the data above.

Homework
• Use the population data to create a Back to Back stem and leaf plot to compare the populations of the 17 most populous cities in the United States based on the 2009 estimate.