Range rule of thumb and standard deviation

Project 1 Instructions

Please also pay close attention to any additional specifications provided by your professor. Professors often will clarify their expectations regarding the format and presentation of your submission.

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 Deviation RROT 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

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77

77

77

123

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123

123

123

Actual Standard deviation = RROT Estimate = % Error =

b. Data Set 2: 1 outlier

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91

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92

92

170

Actual Standard deviation = RROT Estimate = % Error =

c. Data Set 3: 2 outliers

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96

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152

Actual Standard deviation = RROT Estimate = % Error =

d. Data Set 4: Normal (Bell-Shaped) Distribution

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77

84

91

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103

109

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138

Actual Standard deviation = RROT Estimate = % Error =

e. Data Set 5: Uniform Distribution (evenly-spaced values)

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81

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105

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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 Module/Week 3.