Week of 4/11/11

Day 3

Homework review and correction

At this time take out your homework so that we can correct it.

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 place-value position are then used to form the leaves.

28 4

StemLeaf

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.

= 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

Stem LeafNotice that the data (numerical facts) are numbers between 57-98. Create the stem by listing numbers from 5-9.

Notice that the data (numerical facts) are numbers between 57-98. Create the stem by listing numbers from 5-9.

5

6

7

8

9

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.

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.

6 9

5

8

7 4

2 1

5

3 0

2

5

8

3

8

2

7

0

1

Stem Leaf

5

6

7

8

9

7 7 8 0 3

0 2 5 5 6 9

1 1 2 3 5

2 4 7 8

Rearrange the leaf in numerical order from least to greatest

Rearrange the leaf in numerical order from least to greatestKey: 7 9 means 79Key: 7 9 means 79

A key should be included when making a stem-and-leaf plot.

A key should be included when making a stem-and-leaf plot.

Period 2: 57 60 88 85 79 70 65 98 97 59 58 65 62 77 77 75 73 69 82 81

Stem Leaf

Notice that the data (numerical facts) are numbers between 57-98. Create the stem by listing numbers from 5-9.

Notice that the data (numerical facts) are numbers between 57-98. Create the stem by listing numbers from 5-9.

5

6

7

8

9Match 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.

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.

9 0

8

7

8 7

5 2

7

0 5

1

7

9

3

9

2

8

5

5

Stem Leaf5

6

7

8

9

7 8 9 0 2 5 5 9

0 3 5 7 7 9

1 2 5 8

7 8

Rearrange the leaf in numerical order from least to greatest

Rearrange the leaf in numerical order from least to greatest

Key: 7 9 means 79Key: 7 9 means 79

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 1

5

6

7

8

9

7 8 9

0 2 5 5 9

0 3 5 7 7 9

1 2 5 8

7 8

Stem Leaf - period 25

6

7

8

9

7 7 8

0 3

0 2 5 5 6 9

1 1 2 3 5

2 4 7 8

Key: 7 9 means 79Key: 7 9 means 79

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 15

6

7

8

9

7 8 9

0 2 5 5 9

0 3 5 7 7 9

1 2 5 8

7 8

Stem Leaf - period 25

6

7

8

9

7 7 8

0 3

0 2 5 5 6 9

1 1 2 3 5

2 4 7 8

Key: 7 9 means 79Key: 7 9 means 79

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 1

5

6

7

8

9

7 8 9

0 2 5 5 9

0 3 5 7 7 9

1 2 5 8

7 8

Stem Leaf - period 25

6

7

8

9

7 7 8

0 3

0 2 5 5 6 9

1 1 2 3 5

2 4 7 8

Key: 7 9 means 79Key: 7 9 means 79

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 LeafNotice that the data (numerical facts) are numbers between 42-69. Create the stem by listing numbers from 4-6.

Notice that the data (numerical facts) are numbers between 42-69. Create the stem by listing numbers from 4-6.

4

5

6

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.

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.

9

07

9

1

77 7 1

6

68

8

4 42

8

41

0

7

45

2

1 6 15 4 1

5 0

3

5 6

2

2

1 9 4 Key: 5 7 means 57Key: 5 7 means 57

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

0 1 1 1 2 4 4 5 8 9

Stem Leaf

4

5

6

Rearrange the leaf in numerical order from least to greatest

Rearrange the leaf in numerical order from least to greatest

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)

Key: 5 7 means 57Key: 5 7 means 57

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

0 1 1 1 2 4 4 5 8 9

StemLeaf: Age of United States Presidents at their First Inauguration (through the 40th Presidency)

4

5

6

Rearrange the leaf in numerical order from least to greatest

Rearrange the leaf in numerical order from least to greatest

It is easy to interpret or analyze information from the Stem-and-Leaf.

1. How many presidents were 51 years old at their inauguration?

2. What age is the youngest president to be inaugurated?

3. What is the age of the oldest president to be inaugurated?

4. How many presidents were 40-49 years old at their inauguration?

44

4242

6969

77

Key: 5 7 means 57Key: 5 7 means 57

28 4

Stem Leaf

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.

= 2847

Leaf

= 287

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.

Back to back stem and leaf plots

Number of rainy days in a year, Texas cities:67 69 84 73 77 79 63 49 96 06 63 52 105 59 82 90 79 71Number of rainy days in a year, California cities: 37 29 90 117 44 32 35 35 93 75 58 42 62 67 31 45

Homework quiz

Make a back-to-back stem-and-leaf plot of these two data sets. Then find the median and range

of the data sets. Which state is rainier?