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Displaying & Analyzing Data Stem-and-leaf Plot Box-and-Whisker Plot Venn Diagrams Statistics: The branch of mathematics that deals with collecting, organizing, analyzing or interpreting data. Data: Numerical facts or 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. 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 4 Leaf 9 8 6 9 7 2 3 5 7 7 7 8 7 4 1 0 2 6 4 0 5 4 1 6 5 1 4 1 5 6 2 6 1 1 8 4 5 0 2 1 9 4 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 Leaf Rearrange the leaf in numerical order from least to greatest 4 2 3 6 7 8 9 9 5 0 0 1 1 1 1 2 2 4 4 4 4 5 5 5 6 6 6 7 7 7 7 8 6 0 1 1 1 2 4 4 5 8 9 It is easy to interpret or analyze information from the Stemand-Leaf. 1. How many presidents were 51 years old at their inauguration? 4 2. What age is the youngest president to be inaugurated? 42 3. What is the age of the oldest president to be inaugurated? 69 4. How many presidents were 40-49 years old at their inauguration? 7 Stem Leaf: Age of United States Presidents at their First Inauguration (through the 40th Presidency) 4 2 3 6 7 8 9 9 5 0 0 1 1 1 1 2 2 4 4 4 4 5 5 5 6 6 6 7 7 7 7 8 6 0 1 1 1 2 4 4 5 8 9 Data Displays A box-and-whisker plot shows how data is distributed by using the median, upper and lower quartiles, and the greatest and least values in the data set. 17, 18, 19, 21, 24,26, 27 The lower quartile (LQ) is the median of the lower half of the data. The LQ is 18. The upper quartile (UQ) is the median of the upper half of the data. The UQ is 26. ___ __ 16 17 18 19 20 21 22 23 24 25 26 27 28 Make a Box & Whisker Plot 76, 78, 82, 87, 88, 88, 89, 90, 91, 95 88 Find the median of this segment (LQ) LQ = 82 Find the median of this segment. UQ = 90 Lower Quartile (LQ) Least Value 76, 65 78, 70 82, 75 Middle Quartile 87, 88, 80 88, 85 Upper Quartile 89, 90, 90 91, 95 Now for the box and whisker Greatest Value 95 100 105 Lower Quartile (LQ) Least Value 76, 65 78, 70 82, 75 Middle Quartile 87, 88, 80 88, 85 Upper Quartile 89, 90, 90 Greatest Value 91, 95 95 100 105 What number represents 25% of the data? LQ 82 What number represents 50% of the data? Median 88 What number represents 75% of the data? UQ 90 Venn Diagrams Content Standard: Begin to identify information in a Venn diagram Click for the next screen. The diagram shows the results of your survey on ice cream preferences for 23 friends. How many of your friends liked chocolate and/or vanilla ice cream? How many students are not in the diagram? Why? 13 1 8 Click for an answer. How many students are not in the diagram? Why? 23 One student is not in the diagram. He must not like chocolate or vanilla ice cream. -22 1 13 1 8 The End. Stem and Leaf Plot Stem and leaf plots are used as a quick way of seeing how many pieces of data fall in various ranges. The reader can quickly tell: - the range - the mode Stem and leaf plots have a title, a stem, and leaves A key is used to explain how to read the stem and leaves. Box - and - Whisker Plot Displays large set of data. Gives general idea of how data clusters. Graph includes: - Title - Labeled intervals - Box between lower and upper quartiles - Whiskers from quartiles to extremes - Median, quartiles and whiskers labeled Displaying & Analyzing Data Stem-and-leaf Plot Box-and-Whisker Plot Venn Diagrams