3rd Edition

ISBN: 9780135231548

Author: Gould

Publisher: PEARSON C

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Textbook Question

Chapter 3, Problem 96CRE

Children’s Heights Mrs. Diaz has two children: a 3-year-old boy 43 inches tall and a 10-year-old girl 57 inches tall. Three-year-old boys have a mean height of 38 inches and a standard deviation of 2 inches, and 10-year-old girls have a mean height of 54.5 inches and a standard deviation of 2.5 inches. Assume the distributions of boys’ and girls’ heights are unimodal and symmetric. Which of Mrs. Diaz’s children is more unusually tall for his or her age and gender? Explain, showing any calculations you perform. (Source: www.kidsgrowth.com)

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 95CRE

Chapter 3, Problem 97CRE

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Chapter 3 Solutions

INTRODUCTORY STAT. W/MYLAB MATH>CUSTOM<

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Solution Summary: The author identifies the child who is unusually tall for his or her age among the two children of Mrs. Diaz.

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