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1. [0.6/0.6 Points] PREVIOUS ANSWERS AUFEXC4 13.1.010.MI. 1/100 Submissions Used MY NOTES ASK YOUR TEACHER DETAILS Find the mean, the median, and the mode(s), if any, for the given data. Round noninteger means to the nearest tenth. (If there is more than one mode, enter your answer as a comma-separated list. If an answer does not exist, enter DNE.) −8.1, −2.6, 4.5, 4.5, 6.6, 8.9, 9.5 mean median mode(s) Additional Materials Tech Guide: Excel Tech Guide: TI-83/84 Tech Guide: TI-Nspire On a reading test, Shaylen's score of 455 was higher than the scores of 4246 of the 7244 students who took the test. Find the percentile, rounded to the nearest percent, for Shaylen's score.59 th percentile 8/14/2021 Week 7: Practice HW 7: 13.1-13.3 - MATH 115, section D04, Summer 1 2021 | WebAssign https://www.webassign.net/web/Student/Assignment-Responses/last?dep=26921981 2/22 The following tables list the ages of female and male actors when they starred in their award-winning Best Actor performances. (A graphing calculator is recommended.) Ages of Best Female Actor Award Recipients 62 55 45 78 22 71 57 21 79 70 21 34 40 53 77 21 56 69 28 26 36 71 55 46 48 31 59 76 37 52 79 32 43 73 Ages of Best Male Actor Award Recipients 62 75 53 59 66 40 72 64 44 51 71 43 74 63 61 49 39 49 72 67 43 52 73 56 34 52 66 41 73 38 70 39 51 32 (a) Find the mean and the sample standard deviation of the ages of the female recipients. Round each result to the nearest tenth. mean 50.7 50.7 yr sample standard deviation 19.3 19.3 yr (b) Find the mean and the sample standard deviation of the ages of the male recipients. Round each result to the nearest tenth. mean 56.4 55.7 yr sample standard deviation 13.3 13.3 yr (c) Which of the two data sets has the larger mean?female actors male actors Which of the two data sets has the larger standard deviation? female actors male actors Consider the following. 5, 25, 6, 12, 13, 26 Compute the population standard deviation of the numbers. (Round your answer to two decimal place.)8.30 (a) Double each of your original numbers and compute the standard deviation of this new population. (Round your answer to two decimal place.)16.60 (b) Use the results of part (a) and inductive reasoning to state what happens to the standard deviation of a population when each data item is multiplied by a positive constant k.The standard deviation is divided by k. The standard deviation is multiplied by k. The standard deviation is unchanged. The standard deviation is multiplied by -k. The standard deviation is k. A survey of 10 fast-food restaurants noted the number of calories in a mid-sized hamburger. The results are given in the table below. Calories in a mid-sized hamburger 514506503499497505458479463514 Find the mean and sample standard deviation of these data. Round to the nearest hundredth. mean20.17 493.80 sample standard deviation Additional Materials Tech Guide: Excel Tech Guide: TI-83/84 Tech Guide: TI-Nspire Another measure of central tendency for a set of data is called the midrange. The midrange is defined as the value that is halfway between the minimum data value and the maximum data value. That is, Midrange = minimum value + maximum value . 2 The midrange is often stated as the average of a set of data in situations in which there are a large amount of data and the data are constantly changing. Many weather reports state the average daily temperature of a city as the midrange of the temperatures achieved during that day. For instance, if the minimum daily temperature of a city was 60° and the maximum daily temperature was 90°, then the midrange of the temperatures is 60° + 90° = 75°. 2 During a two-minute period, the temperature in a town increased from a low of −6°F to a high of 49°F. Find the mid-range of the temperatures during this two-minute period.21.5 °F The table below shows the numbers of bushels of barley cultivated per acre for 12 one-acre plots of land for two different strains of barley, PHT-34 and CBX-21. PHT-34 CBX-21 42 55 49 47 47 43 38 45 46 46 44 50 50 47 46 59 46 52 45 50 44 48 43 52 Using the same scale, draw a box-and-whisker plot for each of the two data sets, placing the PHT-34 plot below the CBX-21 plot. Write a valid conclusion based on the data. The median number of bushels cultivated per acre for CBX-21 is approximately equal to the median number of bushels cultivated per acre for PHT-34. The maximum number of bushels cultivated per acre for PHT-34 is approximately equal to the median number of bushels cultivated per acre for CBX-21. The maximum number of bushels cultivated per acre for CBX-21 is approximately equal to the median number of bushels cultivated per acre for PHT-34. The minumum number of bushels cultivated per acre for PHT-34 is approximately equal to the median number of bushels cultivated per acre for CBX-21. Additional Materials Tech Guide: TI-83/84 Tech Guide: TI-Nspire 8/14/2021 Week 7: Practice HW 7: 13.1-13.3 - MATH 115, section D04, Summer 1 2021 | WebAssign https://www.webassign.net/web/Student/Assignment-Responses/last?dep=26921981 10/22 Stem-and-Leaf Diagrams The relative position of each data value in a small set of data can be graphically displayed by using a stem-and-leaf diagram. For instance, consider the following history test scores. 65, 72, 96, 86, 43, 61, 75, 86, 49, 68, 98, 74, 84, 78, 85, 75, 86, 73 In the stem-and-leaf diagram below, we have organized the history test scores by placing all of the scores that are in the 40s in the top row, the scores that are in the 50s in the second row, the scores that are in the 60s in the third row, and so on. The tens digits of the scores have been placed to the left of the vertical line. In this diagram, they are referred to as stems. The ones digits of the test scores have been placed in the proper row to the right of the vertical line. In this diagram, they are the leaves. It is now easy to make observations about the distribution of the scores. Only two of the scores are in the 90s. Six of the scores are in the 70s, and none of the scores are in the 50s. The lowest score is 43, and the highest is 98. A Stem-and-Leaf Diagram of a Set of History Test Scores Stems Leaves 4 3 9 5 6 1 5 8 7 2 3 4 5 5 8 8 4 5 6 6 6 9 6 8 Legend: 8|6 represents 86 The choice of how many leading digits to use as the stem will depend on the particular data set. For instance, consider the following data set, in which a travel agent has recorded the amount spent by customers for a cruise. Amount Spent for a Cruise, Summer of 2012 $3600 $4700 $7200 $2100 $5700 $4400 $9400 $6200 $5900 $2100 $4100 $5200 $7300 $6200 $3800 $4900 $5400 $5400 $3100 $3100 $4500 $4500 $2900 $3700 $3700 $4800 $4800 $2400 One method of choosing the stems is to let each thousands digit be a stem and each hundreds digit be a leaf. If the stems and leaves are assigned in this manner, then the notation 2|1, with a stem of 2 and a leaf of 1, represents a cost of $2100, and 5|4 represents a cost of $5400. A stem-and-leaf diagram can now be constructed by writing all of the stems in a column from smallest to largest to the left of a vertical line and writing the corresponding leaves to the right of the line. See the diagram below. Amount Spent for a Cruise Stems Leaves 2 1 1 4 9 3 1 1 6 7 7 8 4 1 4 5 5 7 8 8 9 5 2 4 4 7 9 6 2 2 7 2 3 8 9 4 Legend: 7|3 represents $7300 Sometimes two sets of data can be compared by using a back-to-back stem-and-leaf diagram, in which common stems are listed in the middle column of the diagram. Leaves from one data set are displayed to the right of the stems, and leaves from the other data set are displayed to the left. For instance, the back-to-back stem-and-leaf diagram below shows the test scores for two classes that took the same test. It is easy to see that the 8 A.M. class did better on the test because it had more scores in the 80s and 90s and fewer scores in the 40s, 50s, and 60s. The number of scores in the 70s was the same for both classes. Biology Test Scores 8 A.M. class 10 A.M. class 2 4 5 8 7 5 6 7 9 9 5 8 6 2 3 4 8 1 2 3 3 3 7 8 7 1 3 3 5 5 6 8 4 4 5 5 6 8 8 9 8 2 3 6 6 6 2 4 5 5 8 9 4 5 Legend: 3|7 represents 73 Legend: 8|2 represents 82 Watch the video below then answer the question. Stem-and-Leaf Diagrams Construct a back-to-back stem-and-leaf diagram for the winning and losing scores given in the table below. (Enter numbers from smallest to largest separated by spaces. Enter NONE for stems with no values.) Super Bowl Results, 1967–2011 35–10 33–14 16–7 23–7 16–13 24–3 14–7 24–7 16–6 21–17 32–14 27–10 35–31 31–19 27–10 26–21 27–17 38–9 38–16 46–10 39–20 42–10 20–16 55–10 20–19 37–24 52–17 30–13 49–26 27–17 35–21 31–24 34–19 23–16 34–7 20–17 48–21 32–29 24–21 21–10 29–17 17–14 27–23 31–17 31–25 Winning Scores vs. Losing Scores Winning Losing 2 5 2 6 8 9 0 1 1 1 1 2 2 3 4 4 5 5 5 7 8 8 9 5 4 3 none none 1 0 0 0 1 1 3 3 4 4 4 6 7 7 7 7 7 9 2 0 1 1 1 1 3 4 4 5 6 9 4 6 6 6 7 1 0 0 0 0 0 0 0 3 3 4 4 4 6 6 6 7 7 7 7 7 7 7 9 9 9 none 0 3 6 7 7 7 7 7 9 What information is revealed by your diagram?Most of the winning scores are in the 20s and 30s, whereas most of the losing