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Student GPAs Consider the set of all students enrolled in your statistics course this term. Suppose you're interested in learning about the current grade point averages (GPAs) of this group. 3. Define the population and variable of interest. b. Is the variable qualitative or quantitative? c. Suppose you determine the GPA of every member of the class. Would this determination represent a census or a sample? d. Suppose you determine the GPA of 10 members of the class. Would this determination represent a census or a sample? e. If you determine the GPA of every member of the class and then calculate the average, how much reliability does your calculation have as an "estimate" of the class average GPA? f. If you determine the GPA of 10 members of the class and then calculate the average, will the number you get necessarily be the same as the average GPA for the whole class? On what factors would you expect the reliability of the estimate to depend? g. What must be true in order for the sample of 10 students you select from your class to be considered a random sample?Medicinal value of plants. Sea buckthorn (Hippophae), a plant that typically grows at high altitudes in Europe and Asia, has been found to have medicinal value. The medicinal properties of berries collected from sea buckthorn were investigated in Academia Journal of Medicinal Plants (Aug. 2013). The following variables were measured for each plant sampled. Identify each as producing quantitative or qualitative data. a. Species of sea buckthom (H. rhamnoides, H. gyantsensis, H. neurocarpa, H. tibetana, or H. salicifolia) b. Altitude of collection location (meters) c. Total flavonoid content in berries (milligrams per gram)Use the applet entitled Mean versus Median to find the mean and median of each of the three data sets presented in Exercise 2 59. For each data set, set the lower limit to a number less than all of the data, set the upper limit to a number greater than all of the data, and then click on Update. Click on the approximate location of each data item on the number line. You can get rid of a point by dragging it to the trash can. To clear the graph between data sets, simply click on the trash can. 3. Compare the means and medians generated by the applet with those you calculated by hand in Exercise 2.59. If there are differences, explain why the applet might give values slightly different from the hand-calculated values. b. Despite providing only approximate values of the mean and median of a data set, describe some advantages of using the applet to find those values. (Reference Exercise 2.50) Calculate the mean, median, and mode for each of the following samples: a. 7, -2 3, 3, 0. 4 b. 2. 3, 5. 3, 2, 3. 4, 3, 5, 1, 2. 3, 4 C. 51, 50, 47. 50, 48. 41, 59, 68, 45, 37Use the applet Mean versus Median to study the effect that an extreme value has on the difference between the mean and median. Begin by setting appropriate limits and plotting the following data on the number line provided in the applet: 0 6 7 7 8 8 8 9 9 10 a. Describe the shape of the distribution and record the value of the mean and median. On the basis of the shape of the distribution, do the mean and median have the relationship that you would expect? b. Replace the extreme value of 0 with 2. then 4, and then 8. Record the mean and median each time. Describe what is happening to the mean as 0 is replaced, in turn, by the higher numbers stated. What is happening to the median? How is the difference between the mean and the median changing? c. Now replace 0 with 8. What values does the applet give you for the mean and the median? Explain why the mean and the median should now be the same.Complete the following table: Grade on Statistics Exam | Frequency | Relative Frequency A: 90-100 108 B: 80-89 36 C: 85-79 90 D: 50-84 30 F: Below 50 28 Total 200 1.00Interactions in a children's museum. The nature of child-led and adult-led interactions in a children's museum was investigated in Early Childhood Education Journal (Mar. 2014). Interactions by visitors to the museum were classified as (1) show-and-tell, (2) learning. (3) teaching. (4) refocusing. (5) participatory play. (8) advocating. or (7) disciplining. Over a 3-month period, the researchers observed 170 meaningful interactions, of which 81 were led by children and 80 were led by adult caregivers. The number of interactions observed in each category is provided in the accompanying table. Use side-by-side bar graphs to compare the interactions led by children and adults. Do you observe any trends? Type of Interaction Child-Led Adult-Led Show-and-tell 26 Learning 21 Teaching 10 Refocusing 21 Participatory Play 12 Advocating Disciplining Tolals 81 Source: McMunn-Dooky C, and Welch, M. M. "Nature of interactions among young children and adult caregivers in a children's muscum." from Figure 21Motivation and right-oriented bias. Evolutionary theory suggests that motivated decision makers tend to exhibit a right-oriented bias. (For example, if presented with two equally valued brands of detergent on a supermarket shelf, consumers are more likely to choose the brand on the right.) In Psychological Science (November 2011), researchers tested this theory using data on all penalty shots attempted in World Cup soccer matches (a total of 204 penalty shots). The researchers believe that goalkeepers, motivated to make a penalty shot save but with little time to make a decision, will tend to dive to the right. The results of the study (percentages of dives to the left, middle, or right) are provided in the table. Note that the percentages in each row. corresponding to a certain match situation, add to 100%. Construct side-by-side bar graphs showing the distribution of dives for the three match situations. What inferences can you draw from the graphs? Match Situation Dive Left Stay Middle Dive Right Team behind 29% 71% Tied 49% Team ahead 51% 48% Sauce: Rockes, M. cial. "The right side? Under time pressure, approach molinvation leads to right-oriented his"Packedopal Saran, Val. ). No. II. Nov 2011 ( adapted from Figure 1).Suppose you're given a data set that classifies each sample unit into one of four categories: A, B. C. or D. You plan to create a computer database consisting of these data, and you decide to code the data as A = 1, B = 2. 0 = 3, and D = 4. Are the data consisting of the classifications A, B. C. and D qualitative or quantitative? After the data are input as 1, 2. 3, or 4, are they qualitative or quantitative? Explain your answers.STEM experiences for girls. The National Science Foundation (NSF) promotes girls' participation in informal science, technology, engineering. and mathematics (STEM) programs. What has been the impact of these informal STEM experiences? This was the question of interest in the published study Cascading Influences: Long-Term Impacts of Informal STEM Experiences for Girls (Mar. 2013). A sample of 159 young women who recently participated in a STEM program were recruited to complete an online survey. Of these, only 27% felt that participation in the STEM program increased their interest in science. a. Identify the population of interest to the researchers. b. Identify the sample. c. Use the information in the study to make an inference about the relevant population.Drafting NFL quarterbacks. The Journal of Productivity Analysis (Vol. 35, 2011) published a study of how successful National Football League (NFL) teams are in drafting productive quarterbacks. Data were collected for all 331 quarterbacks drafted over a 38-year period. Several variables were measured for each QB, including draft position (one of the top 10 players picked, selection between picks 11-50. or selected after pick 50), NFL winning ratio(percentage of games won), and QB production score (higher scores indicate more productive QBs). The researchers discovered that draft position was only weaklyrelated to a quarterback's performance in the NFL. They concluded that "quarterbacks taken higher [in the draft] do not appear to perform any better." a. What is the experimental unit for this study? b. Identify the type (quantitative or qualitative) of each variable measured. C. Is the study an application of descriptive or inferential statistics? Explain