Consider the following four data sets in the table below. Complete parts (a) through (g) below. Click the icon to view the four data sets. a. Compute the mean of each data set. x (Data Set I) x (Data Set III) = Data set x (Data Set II) X (Data Set IV) x (Type integers or decimals. Do not round.) b. Although the four data sets have the same means, in what respect are they quite different? OA. The amount of variation within each data set is the same among the data sets, but with different values. OB. Each data set has a unique median. OC. The amount of variation within each data set differs among the data sets. OD. The data sets are not different as the four data sets are identical. c. Which data set appears to have the least variation? the greatest variation? = 1 = 0 appears to have the least variation. Data set d. Compute the range of each data set Range (Set I) = 7 Range (Set III) = (Type integers or decimals. Do not round.). Click to select your answer(s). Range (Set II) Range (Set IV) -1 = appears to have the greatest variation. Data Sets Data Set I 1 1 2 2 5 5 8 8 9 9 Data Set II 9 1 1 1 4 1 1 9 9 9 9 Print Data Set III 5 5 5 5 5 5 5 5 5 5 Done Data Set IV 5 6 6 7 10 2 3 3 4 4 Consider the following four data sets in the table below. Complete parts (a) through (g) below. Click the icon to view the four data sets. Kange (Set III) = (Type integers or decimals. Do not round.) e. Use the defining formula to compute the sample standard deviation of each data set. Range (Set IV) = Data Sets Click to select your answer(s). Data Set I 5 8 1 1 2 2 5 8 9 9 A. The range distinguishes spread better because it shows that the sets are structurally similar, because their extrema are equally spread out. OB. The standard deviation distinguishes spread better because it is resistant to outliers, and is therefore more robust than the range. OC. The range distinguishes spread better because it shows that having different standard deviations doesn't imply that the means must be different. OD. The standard deviation distinguishes spread better because it shows that the sets are structurally different, despite having similar ranges and means. g. Are your answers from parts (c) and (e) consistent? A. No, because the minimum and maximum standard deviations do not correspond to the data sets with the least and greatest variation, respectively. OB. No, because it is not necessary that greater variation and greater standard deviation are correlated. OC. Yes, because there is a correlation between the range and the standard deviation of the data sets. OD, Yes, because the minimum and maximum standard deviations correspond to the data sets with the least and greatest variation, respectively. Data Set II 1 1 1 1 1 1 9 9 s (Set I) s (Set II) s (Set III) =7 s (Set IV) = (Type integers or decimals. Round to one decimal place as needed.) f. From your answers to parts (d) and (e), which measure of variation better distinguishes the spread in the four data sets: the range or the standard deviation? Explain your answer. 9 9 9 Data Set III 5 5 5 5 5 5 5 5 5 5 Print Done Data Set IV 2 5 3 6 3 6 4 7 4 10