Essentials of Statistics for the Behavioral Sciences

8th Edition

ISBN: 9781133956570

Author: Frederick J Gravetter, Larry B. Wallnau

Publisher: Cengage Learning

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Textbook Question

Chapter 4, Problem 23P

Within a population, the difference that exist from one person to another are often called diversity. Researchers comparing cognitive skills for younger adults and older adults, typically find greater difference (greater diversity) in the older population (Morse. 1993). Following are typical data showing problem-Solving scores for two groups of participants.

Older Adults (average age 72)	Younger Adults (average age 31)
9 4 7 3 8	7 9 6 7 8
6 2 8 5 4	6 7 6 6 8
7 5 2 6 6	9 7 8 6 9

a. Compute the mean, the variance, and the standard deviation for each group.
b. Is one group or scores noticeably more variable (more diverse) than the other?

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 4, Problem 22P

Chapter 4, Problem 24P

Chapter 4 Solutions

Essentials of Statistics for the Behavioral Sciences

Ch. 4.3 - Brief explain what is measured by the standard...Ch. 4.3 - The deviation scores are calculated for each...Ch. 4.3 - What is the standard deviation for the following...Ch. 4.3 - Calculate the variance for the following...Ch. 4.3 - Find the sum of the squared deviations, SS, for...Ch. 4.3 - a. Sketch a histogram showing the frequency...Ch. 4.4 - a. Sketch a histogram showing the frequency...Ch. 4.4 - For the following set of scores: 1, 5, 7, 3, 4 a....Ch. 4.4 - Prob. 3LC Ch. 4.5 - Explain the difference between a biased and an...

Ch. 4.5 - In a population with a mean of = 50 and a...Ch. 4.5 - A population has a mean of . = 70 and a standard...Ch. 4 - In words, explain what is measured by each of the...Ch. 4 - Can SS ever have a value less than zero? Explain...Ch. 4 - Is it possible to obtain a negative value for the...Ch. 4 - What does it mean for a sample to have a standard...Ch. 4 - Explain why the formula for sample variance is...Ch. 4 - A population has a mean of = 80 and a standard...Ch. 4 - On an exam with a mean of M = 78, you obtain a...Ch. 4 - Calculate the mean and SS (sum of squared...Ch. 4 - For the following population of N = 6 scores: 3 1...Ch. 4 - For the following sample of n = 7 scores: 8 6 5 2...Ch. 4 - For the following population of N = 6 scores: 11 0...Ch. 4 - The range is completely determined by the two...Ch. 4 - A population has a mean of = 30 and a standard...Ch. 4 - a. After 3 points have heen aikicd to every score...Ch. 4 - For the following sample of n = 4 scores: 82, 88,...Ch. 4 - For the following sample of n = 8 scores: 0, 1,...Ch. 4 - For the data in the following sample: 81515 a....Ch. 4 - Calculate the mean and SS (sum of squared...Ch. 4 - Calculate SS, variance, and standard deviation for...Ch. 4 - Calculate SS, variance, and standard deviation for...Ch. 4 - Calculate SS, variance, and standard deviation for...Ch. 4 - In an extensive study involving thousands of...Ch. 4 - Within a population, the difference that exist...Ch. 4 - In the previous problem we noted that the...Ch. 4 - a. What is the general goal for descriptive...

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Urban Travel Times Population of cities and driving times are related, as shown in the accompanying table, which shows the 1960 population N, in thousands, for several cities, together with the average time T, in minutes, sent by residents driving to work. City Population N Driving time T Los Angeles 6489 16.8 Pittsburgh 1804 12.6 Washington 1808 14.3 Hutchinson 38 6.1 Nashville 347 10.8 Tallahassee 48 7.3 An analysis of these data, along with data from 17 other cities in the United States and Canada, led to a power model of average driving time as a function of population. a Construct a power model of driving time in minutes as a function of population measured in thousands b Is average driving time in Pittsburgh more or less than would be expected from its population? c If you wish to move to a smaller city to reduce your average driving time to work by 25, how much smaller should the city be?

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Solution Summary: The author explains the mean and standard deviation for older and younger adults in the table.

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Chapter 4 Solutions