What is the branch of mathematics that deals with collecting organizing and interpreting of data?

Presentation on theme: "Statistics: The branch of mathematics that deals with collecting, organizing, and analyzing or interpreting data. Data: Numerical facts or numerical information."— Presentation transcript:

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2 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.

3 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.

4 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. 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

5 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

6 Period 1: 76 79 85 58 97 94 82 81 75 63 60 92 75 98 83 58 72 57 70 81 StemLeaf Notice that the data (numerical facts) are numbers between 57-98. Create the stem by listing numbers from 5-9. 5678956789 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. 69 5 8 74 21 5 30 2 5 8 3 8 2 7 0 1 StemLeaf 5678956789 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 Key: 7 9 means 79 A key should be included when making a stem- and-leaf plot.

7 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. 5678956789 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. 90 8 7 87 52 7 05 1 7 9 3 9 2 8 5 5 StemLeaf 5678956789 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 Key: 7 9 means 79

8 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 StemLeaf - period 1 5678956789 7 8 9 0 2 5 5 9 0 3 5 7 7 9 1 2 5 8 7 8 StemLeaf - period 2 5678956789 7 7 8 0 3 0 2 5 5 6 9 1 1 2 3 5 2 4 7 8 Key: 7 9 means 79

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. StemLeaf - period 1 5678956789 7 8 9 0 2 5 5 9 0 3 5 7 7 9 1 2 5 8 7 8 StemLeaf - period 2 5678956789 7 7 8 0 3 0 2 5 5 6 9 1 1 2 3 5 2 4 7 8 Key: 7 9 means 79

10 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. StemLeaf - period 1 5678956789 7 8 9 0 2 5 5 9 0 3 5 7 7 9 1 2 5 8 7 8 StemLeaf - period 2 5678956789 7 7 8 0 3 0 2 5 5 6 9 1 1 2 3 5 2 4 7 8 Key: 7 9 means 79

11 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 40 th presidency) StemLeaf Notice that the data (numerical facts) are numbers between 42- 69. Create the stem by listing numbers from 4-6. 456456 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 7771 6 68 8 442 8 41 0 7 45 2 161541 50 3 56 2 2 194 Key: 5 7 means 57

12 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 456456 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 40 th presidency) Key: 5 7 means 57

13 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 40 th Presidency) 456456 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? 23 42 69 7 7 Key: 5 7 means 57