The Essentials of Statistics: A Tool for Social Research

4th Edition

ISBN: 9781305802698

Author: Joseph F. Healey

Publisher: Cengage Learning US

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Concept explainers

Inverse Normal Distribution

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 3.11P

SOC The following table lists the approximate number of cars per 1000 population for 15 nations. Compute the mean and median for these data. Which is greater in value? Is there a positive skew in the data? How do you know?

Nation	Number of Motor Vehicles per 1000 Population (2009)
United States	786
Germany	588
Canada	608
Japan	588
Australia	703
Israel	330
Russia	271
Mexico	278
Tunisia	130
Bolivia	87
China	69
Niger	8
Kenya	25
Thailand	172
India	18
Mean =
Median =

Source: World Bank, 2014. Retrieved from http://data.worldbank.org/indicator/lS.VEH.NVEH.P3

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 Solutions

The Essentials of Statistics: A Tool for Social Research

Ch. 3 - SOCA variety of information has been gathered from...Ch. 3 - A variety of information has been collected for...Ch. 3 - You have been observing the local Democratic Party...Ch. 3 - The following table presents the annual...Ch. 3 - SOC Data have been gathered on four variables for...Ch. 3 - SOC The following tables list the median family...Ch. 3 - Find the appropriate measure of central tendency...Ch. 3 - SOC The accompanying table gives scores on four...Ch. 3 - SOC The college administration is considering a...Ch. 3 - SOC As the head of a social services agency, you...

Ch. 3 - SOC The following table lists the approximate...Ch. 3 - SW Compute the median and mean for both the...Ch. 3 - SOC A sample of 25 freshmen at a major university...Ch. 3 - You have compiled the following information on...Ch. 3 - Professional athletes are threatening to strike...

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Solution Summary: The author calculates the mean and median of 310 cars per 1000 population, which is higher than median, and the positive skewness is due to the high number of vehicles in United States and Australia.

Concept explainers

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Chapter 3 Solutions