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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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Explanation & Answer:

1 Excel Data Sheet

Standard Deviation Project

Tags:

standard deviation

statistics

Data Sets

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