7th Edition

ISBN: 9781111792374

Author: WEIERS

Publisher: Cengage Learning

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Chapter 3, Problem 3.60CE

A law enforcement agency, administering breathalyzer tests to a sample of drivers stopped at a New Year’s Eve roadblock, measured the following blood alcohol levels for the 25 drivers who were stopped:

0.00% 0.08% 0.15% 0.18% 0.02%
0.04 0.00 0.03 0.11 0.17
0.05 0.21 0.01 0.10 0.19
0.00 0.09 0.05 0.03 0.00
0.03 0.00 0.16 0.04 0.10
a. Calculate the mean and standard deviation for this sample.

b. Use Chebyshev’s theorem to determine the minimum percentage of observations that should fall within k = 1.50 standard deviation units of the mean. Do the sample results support the theorem?

c. Calculate the coefficient of variation for these data.

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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Chapter 3, Problem 3.59CE

Chapter 3, Problem 3.61CE

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Solution Summary: The author explains the formula used to calculate the mean and standard deviation of the given sample data.

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