Sample Standard Deviation (10 points): use the Excel function "-stdev.s" (or technology) Range Rule of Thumb (RROT) Estimate (10 points): the formula for the BROT estimate is PROT estimate = Range/4 (where the range = maximum value - minimum value), on the assumption that the Standard Deviation = BROT estimate Percentage Error (% Error) (10 points): The formula used to find the percentage error of the estimate is: % Error = | RRQT Estimate - Standard deviation | / Standard Deviation x 100 =_%. Round answers to two decimal places as needed. Data Set 1: No outliers 77 77 77 77 77 132 132 132 132 132 Actual Standard deviation = 28.99 BROT Estimate = 13.75 %% Error = 52.57 2. Data Set 2: 1 outlier 63 76 76 76 76 77 77 77 77 155 Actual Standard deviation =18.0 BROT Estimate =23 % Error = 27.8 3. Data Set 3: 2 outliers 48 96 98 99 100 100 101 102 114 162 Actual Standard deviation BROT Estimate = To Error- 4. Data Set 4: Normal (Bell-Shaped) Distribution $5 71 78 85 91 97 103 110 119 132 Actual Standard deviation BROT Estimate = % Error - 5. Data Set 5: Uniform Distribution (evenly-spaced values) 61 69 77 85 93 101 109 117 125 133 Actual Standard deviation = BROT Estimate % Error = Summarize what you learned: a) Does the Range Rule of Thumb estimate more often underestimate or overestimate the actual standard deviation? (3 points) b) What is the largest percentage error? (3 points) c) Each of the data sets given above is artificially contrived. If you were to apply the RRQT estimate to a typical real-world data set, about how accurate would you expect it to be (your answer here should be a numerical estimate of the percentage error, based on your previous results)? (4 points)