Essentials of Statistics, Books a la Carte Edition (5th Edition)

5th Edition

ISBN: 9780321926739

Author: Mario F. Triola

Publisher: PEARSON

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Textbook Question

Chapter 3.2, Problem 33BB

Degrees of Freedom Carbon monoxide is measured in San Francisco on five different days, and the mean of those five values is 0.62 parts per million. Four of the values (in parts per million) are 0.3, 0.4, 1.1, and 0.7. (The data are from the California Environmental Protection Agency.)

a. Find the missing value.
b. We need to create a list of n values that have a specific known mean. We are free to select any values we desire for some of the n values. How many of the n values can be freely assigned before the remaining values are determined? (The result is referred to as the number of degrees of freedom.)

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 3.2, Problem 32BSC

Chapter 3.2, Problem 34BB

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Chapter 3 Solutions

Essentials of Statistics, Books a la Carte Edition (5th Edition)

Ch. 3.2 - Employment Data listed below are results from the...Ch. 3.2 - Average The web site IncomeTaxList.com lists the...Ch. 3.2 - Median In an editorial, the Poughkeepsie Journal...Ch. 3.2 - Prob. 4BSC Ch. 3.2 - In Exercises 5-20, find the (a) mean, (b) median,...Ch. 3.2 - In Exercises 5-20, find the (a) mean, (b) median,...Ch. 3.2 - In Exercises 5-20, find the (a) mean, (b) median,...Ch. 3.2 - Prob. 8BSC Ch. 3.2 - In Exercises 5-20, find the (a) mean, (b) median,...Ch. 3.2 - Prob. 10BSC

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Solution Summary: The author explains how the data shows the mean of five different values of carbon monoxide is 0.62 parts per million.

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