MATH 114 Hampton University Standard Deviation Project

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MATH 114
STANDARD DEVIATION, RANGE RULE OF THUMB, AND PERCENTAGE ERROR
PROJECT ASSIGNMENT INSTRUCTIONS
OVERVIEW
Standard deviation is a reliable (and commonly used) measure of variation. Standard deviation
essentially describes the average distance that each data value is away from the mean.
Computing standard deviation by hand can be complicated so you are asked to use Excel to
calculate it for this project. You will also calculate the Range Rule of Thumb (RROT). The
RROT is based on the insight that the range is often approximately four times as large as the
standard deviation. This insight enables you to quickly estimate the standard deviation of a data
set quickly. Lastly, you will calculate the percentage error of each data set. Percent error is the
difference between estimated value (RROT) and the actual value (standard deviation) in
comparison to the actual value and is expressed as a percentage.
INSTRUCTIONS
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. Excel can be used to do the
calculations. For each of the 5 data sets given below to find the following:
• 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 RROT
estimate is RROT estimate = Range/4 (where the range = maximum value –
minimum value), on the assumption that the Standard Deviation  RROT estimate.
• Percentage Error (% Error) (10 points): 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
90
90
90
90
90
Actual Standard deviation =
130
130
130
RROT Estimate =
130
130
% Error =
b. Data Set 2: 1 outlier
68
81
81
81
81
Actual Standard deviation =
82
82
82
RROT Estimate =
82
160
% Error =
c. Data Set 3: 2 outliers
38
86
88
89
90
Actual Standard deviation =
90
91
92
RROT Estimate =
104
152
% Error =
d. Data Set 4: Normal (Bell-Shaped) Distribution
51
67
74
81
87
Actual Standard deviation =
93
99
106
RROT Estimate =
115
128
% Error =
e. Data Set 5: Uniform Distribution (evenly-spaced values)
65
73
81
Actual Standard deviation =
89
97
105
113
RROT Estimate =
121
129
% Error =
137
MATH 114
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)

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Standard Deviation Project

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