18th Edition

ISBN: 9781264293629

Author: Lind

Publisher: MCG

Concept explainers

The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of tw…

Mean, Median, Mode

It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency o…

Z-Scores

A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow compar…

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Textbook Question

Chapter 3, Problem 54E

The mean income of a group of sample observations is $500; the standard deviation is $40. According to Chebyshev’s theorem, at least what percent of the incomes will lie between $400 and $600?

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 53E

Chapter 3, Problem 55E

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Chapter 3 Solutions

STATISTICAL TECH IN BUSN LLW/CONNECT

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The mean income of a group of sample observations is $500; the standard deviation is $40. According to Chebyshev’s theorem, at least what percent of the incomes will lie between $400 and $600?

Solution Summary: The author explains Chebyshev's theorem: the proportion of values that lie within k standard deviations of the mean for any set of observations is at least 1-1k2

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