Question
The Range Rule of Thumb is based on the insight that the range is often approximately 4 times as large as the standard deviation. This
The Range Rule of Thumb is based on the insight that the range is often approximately 4 times as large as the standard deviation. This insight enables you to quickly estimate the standard deviation of a data set by finding the maximum and minimum data values, using them to compute the range, and then dividing this value by 4.
1.Each of the following 5 data sets has a mean close to 100, and a standard deviation in the 20s. Assume that each of these are sample data sets.For each of the 5 data sets given below, use the Excel function "=stdev.s" (or technology) to find the actual sample standard deviation (10 points), compute the estimate given by the Range Rule of Thumb (RROT) Estimate (10 points), and compute the percentage error of the estimate (10 points). The formula for the RROT estimate is RROT estimate = Range/4 (where the range = maximum value - minimum value), on the assumption that the Standard DeviationRROT estimate.The formula used to find the percentage error of the estimate is:
% Error =|RROT Estimate - Standard deviation|/ Standard Deviation 100 = ____ % .
a.Data Set 1: No outliers
68
68
68
68
68
133
133
133
133
133
Actual Standarddeviation =RROT Estimate =% Error =
b.Data Set 2: 1 outlier
68
81
81
81
81
82
82
82
82
160
Actual Standarddeviation =RROT Estimate =% Error =
c.Data Set 3: 2 outliers
38
86
88
89
90
90
91
92
104
152
Actual Standard deviation =RROT Estimate =% Error =
d.Data Set 4: Normal (Bell-Shaped) Distribution
51
67
74
81
87
93
99
106
115
128
Actual Standard deviation =RROT Estimate =% Error =
e.Data Set 5: Uniform Distribution (evenly-spaced values)
65
73
81
89
97
105
113
121
129
137
Actual Standard deviation =RROT Estimate =% Error =
2.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 RROT 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)
Submit your Project 1 by 11:59 p.m. (ET) on Monday of M
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Quantitative Analysis For Management
Authors: Barry Render, Ralph M. Stair, Michael E. Hanna
11th Edition
9780132997621, 132149117, 132997622, 978-0132149112
