Liberty University Standard Deviation Questions

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The Range Rule of Thumb is based on the insight that the range is often approximately 4times as large as the standard deviation. This insight enables youto quickly estimate the standard deviation of a data set byfindingthe maximum and minimum data values, using them to compute the range, and then dividing this valueby 4.

1. Each of the following 5data 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 5data 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

Actual Standard deviation = RROT Estimate =% Error =

b. Data Set 2: 1outlier

Actual Standard deviation = RROT Estimate =% Error =

c. Data Set 3: 2outliers

Actual Standard deviation = RROT Estimate =% Error =

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

Actual Standard deviation = RROT Estimate =% Error =

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

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 youwere to apply the RROT estimate to a typical real-world data set, about how accurate would youexpect it to be(your answer here should be a numerical estimate of the percentage error, based on your previous results)? (4 points)