Statistics: Stem-and-Leaf Plots

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 5 6 7 8 9 7 7 8 6 9 5 5 2 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.

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 5 5 2 9 0 2 5 5 9 9 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: 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

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: 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

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: 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

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 2 6 4 5 4 1 6 5 1 4 1 5 6 2 Key: 5 7 means 57 1 1 8 4 5 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: 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

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? 23 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: 5 7 means 57 0 1 1 1 2 4 4 5 8 9