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Week of 4/11/11 Day 3

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Homework review and correction At this time take out your homework so that we can correct it.

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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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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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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

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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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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.

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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

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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

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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

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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

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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

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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

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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? 4 4 42 69 7 7 Key: 5 7 means 57

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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. = 284 7 Leaf = 287

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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.

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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.

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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 71 Number of rainy days in a year, California cities: 37 29 90 117 44 32 35 35 93 75 58 42 62 67 31 45

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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?

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