e) Is there any data point that should be considered as an outlier for this data set? Explain why. f) What is the percentage of measurements that actually fall within one standard deviation from the mean? 2) Discuss whether the shape you described in (d) makes sense using other descriptive measures. [4](9) Consider nutritional data about a sample of seven breakfast cereals that includes the number of calories per serving and the amount of sugars per serving (in grams). Cereal Calories Sugar Kellogg's All Bran Kellogg's Com Flakes 100 Wheaties 100 Nature's Plan Organic Multigrain Flakes 110 Kellogg's Rice Krispies 130 Post Shredded Wheat Vanilla Almond 190 11 Kellogg's Mini Wheats 200 10 a) Find the sample mean calories per serving and sample mean amount of sugar per serving. b) Find the sample standard deviation for calories per serving and sample standard deviation for amount of sugar per serving. ( Which variable, calories or sugar, offers you more choices relative to the sample mean when you want to select one cereal? Explain.[3](27) As a result of government and consumer pressure, automobile manufacturers in the United States, are deeply involved in research to improve their products' gasoline mileage. One manufacture, hoping to achieve 40 miles per gallon on one of its compact models, measured the mileage obtained by 36 test versions of the model with the following results (rounded to the nearest mile for conve nience): 43 35 41 42 42 38 40 41 41 40 40 41 Ix 1444 42 37 43 40 38 40 38 45 39 41 42 37 S*=2.159458 8644 40 40 44 39 40 37 39 41 39 41 38 40 ox 2. 065292255 In 36 a) Compute the following statistics. Quantity Measurement mean (x) median (7) mode (m) sample standard deviation (s) sample variance (s?) range ( R) coefficient of variation (CV) b) Compute the following statistics. X'min Xmas () Construct the boxplot (box-and-whisker diagram) for the data. 35 50 d) Describe the shape of the distribution of gas mileages of the test versions of the model using the box plot. Explain why you would think that the shape you describe happens with this type of data