3rd Edition

ISBN: 9780135190210

Author: Gould

Publisher: PEARSON CO

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 85CRE

For exercises 3.85 through 3.88, construct two sets of numbers with at least five numbers in each set with the following characteristics:

The means are the same, but the standard deviation of one of the sets is smaller than that of the other. Report the mean and both standard deviations.

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 84CRE

Chapter 3, Problem 86CRE

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For exercises 3.85 through 3.88, construct two sets of numbers with at least five numbers in each set with the following characteristics: The means are the same, but the standard deviation of one of the sets is smaller than that of the other. Report the mean and both standard deviations.

Solution Summary: The author explains that two data sets have the same mean but the standard deviation of one data set is smaller than the other.

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