3rd Edition

ISBN: 9780135163146

Author: Gould

Publisher: PEARSON

Concept explainers

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Textbook Question

Chapter 3, Problem 20SE

Sibling Ages Four siblings are 2, 6, 9, and 10 years old.

a. Calculate the mean of their current ages. Round to the nearest tenth.

b. Without doing any calculation, predict the mean of their ages 10 years from now. Check your prediction by calculating their mean age in 10 years (when they are 12, 16, 19, and 20 years old).

c. Calculate the standard deviation of their current ages. Round to the nearest tenth.

d. Without doing any calculation, predict the standard deviation of their ages 10 years from now. Check your prediction by calculating the standard deviation of their ages in 10 years.

e. Adding 10 years to each of the siblings ages had different effects on the mean and the standard deviation. Why did one of these values change while the other remained unchanged? How does adding the same value to each number in a data set affect the mean and standard deviation?

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 19SE

Chapter 3, Problem 21SE

Chapter 3 Solutions

INTRODUCTORY STATISTICS (LOOSELEAF)

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Solution Summary: The author calculates the mean age of the four siblings for the given data set with the standard deviation (s).

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