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Name __________________________Statistics: Histograms, Stem and Leaf Plots, and Dot Plots These four graphs all display the same data--the Kentucky Derby winning times. The dot plot is a horizontal version of the graph shown in your book. 1. Describe fully in context what each lettered part represents about the data. A B A C D E B E C 17 : 2 D 16 : 5 16 : 000113 15 : 5777777888899 15 : 14 : 14 : 13 : 5 13 : 00111233 12 : 555555555555556667777888888999999 12 : 0001111111111222222222222222222222222222223333333333333334444444444444 11 : 9 (13:5 means a winning time of 135 seconds) 2. What are the similarities and differences of each graph? 3. When might you choose to display data using a stem and leaf plot instead of a histogram? Copyright © 2012 Pearson Education, Inc. Publishing as Addison-Wesley. 4-11 TRIAL MODE − a valid license will remove this message. See the keywords property of this PDF for more information. Name _____________________________________________ Statistics: Frequency Tables 1. Here is a frequency table showing how nuclear power plants are distributed across the United States. a. Explain what the pair (2, 11) in this table represents in the context of the problem. ______________________________________________________ ______________________________________________________ # plants 0 1 2 3 4 5 6 # states 19 12 11 4 2 1 1 b. Find the mean and median and describe these values in context. Mean: Median: 2. Here is a frequency table of the ages of U.S. Presidents when they were first inaugurated into the office. a. Which interval contains the median age of inauguration? b. Estimate the mean age of inauguration of U.S. Presidents (use the center of each interval) Age at inauguration 40-44 45-49 50-54 55-59 60-64 65-69 Number of Presidents 2 7 13 12 7 3 3. Estimate the mean and median of the data shown in this histogram. Copyright © 2012 Pearson Education, Inc. Publishing as Addison-Wesley. 4-13 TRIAL MODE − a valid license will remove this message. See the keywords property of this PDF for more information. Name ______________________________________ Statistics: The 5 Number Summary 1. Pediatricians use percentiles to monitor the height and weight of their patients over time. According to the Centers for Disease Control, the distribution of weights of 5 year old males has the following quartiles: 1st quartile: 37 pounds 2nd quartile: 40 pounds 3rd quartile: 42 pounds a. For each quartile, write a sentence that describes what that quartile means about the weights of 5 year old males. Q1: Q2: Q3: b. What percent of 5 year old males weigh… between 37 and 40 pounds less than 40 pounds more than 40 pounds more than 37 pounds between 40 and 42 pounds less than 37 pounds c. Mark is a 5 year old of average height who weighs 38 pounds. Is his weight also average? Explain your thinking. 2. Here again is the dot plot of the 135 Kentucky Derby winning times. Use the dot plot to separate the dots into quartiles, then draw a box and whisker plot above the dots on the same axis. On the back, describe the shape, center, and spread of the distribution of winning times in context. Copyright © 2012 Pearson Education, Inc. Publishing as Addison-Wesley. 4-15 TRIAL MODE − a valid license will remove this message. See the keywords property of this PDF for more information. Name ______________________________________ Statistics: Standard Deviation A class has been divided into groups of five students each. The groups have completed an independent study project, and at the end they take an individual 20-point quiz. Here are the scores, by group: Group Quiz Scores (out of 20) 1 10 10 10 10 10 2 8 10 10 10 12 3 0 10 10 10 20 4 0 8 10 12 20 5 0 2 10 18 20 6 4 6 8 14 18 Mean Median Range 1. Find the mean and median for each group. How well do these measures of center alone describe the differences among these groups? 2. Find the range for each group. How well does this measure of spread reflect the differences in these distributions? 3. Calculate the standard deviation for each group. Use the table below to organize your calculations. (D = Deviation of that quiz score from the mean for that group) Group 1 D D2 10 10 10 10 10 Score Group 2 D D2 8 10 10 10 12 Score Group 3 D D2 0 10 10 10 20 Score Group 4 D D2 0 8 10 12 20 Score Group 5 D D2 0 2 10 18 20 Score Group 6 D D2 4 6 8 14 18 Score Sum of D2 Divide by n-1 Square root (SD) Copyright © 2012 Pearson Education, Inc. Publishing as Addison-Wesley. 4-17 TRIAL MODE − a valid license will remove this message. See the keywords property of this PDF for more information. Score 4. Make a dot plot of each group’s scores on the scale below. The first two groups are done for you. 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0 Ɣ ƔƔƔƔƔ ƔƔƔ Ɣ 1 2 3 4 5 6 Group 5. Examine the dotplot. How does the standard deviation of each group describe the spread of each group compared to the spread of the other groups? Group 1: Group 2: Group 3: Group 4: Group 5: Group 6: Copyright © 2012 Pearson Education, Inc. Publishing as Addison-Wesley. 4-18 TRIAL MODE − a valid license will remove this message. See the keywords property of this PDF for more information. Name ______________________________________ Statistics: More with Histograms 1. Sketch histograms that meet the following descriptions. Also, describe the shape of each distribution. a) The mean, median, and the mode are almost equal. b) The mean is less than the mean. c) The mean, median and mode are all different from each other. d) The mean and median are almost equal but the mode is different. 2. For each example above, tell whether is is best to describe the data using the mean and the standard deviation or the median and the IQR. 3. Decide whether each set of data below could be displayed in either a bar graph or a histogram. On the back, draw and label that graph, and justify your choice. Set A Set B Height (inches) Number of children 40-44 45-49 50-54 55-59 60-64 4 7 3 1 1 Set C Color frequency of hair Brown Blonde Red Black Shoe size shoes in stock 5 6 7 8 9 44 26 74 62 48 112 234 45 77 Set D Number of commercials during selected TV movies 15, 14, 16, 10, 16, 16, 13, 14, 15, 12, 10, 11, 19, 13, 15 Copyright © 2012 Pearson Education, Inc. Publishing as Addison-Wesley. 4-21 TRIAL MODE − a valid license will remove this message. See the keywords property of this PDF for more information.