2nd Edition

ISBN: 9781259570643

Author: Navidi

Publisher: MCG

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A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.

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Textbook Question

Chapter 3.3, Problem 22E

A fish story: The mean length of one-year-old spotted flounder, in millimeters, is 126 with standard deviation of 18, and the mean length of two-year-old spotted flounder is 162 with a standard deviation of 28. The distribution of flounder lengths is approximately bell-shaped.

a. Anna caught a one-year-old flounder that was 150 millimeters in length. What is the z-score for this length?
b. Luis caught a two-year-old flounder that was 190 millimeters in length. What is the z-score for this length?
c. Whose fish is longer, relative to fish the same age?
d. Joe caught a one-year-old flounder whose length had a z-score of 1.2. How long was this fish?
e. Terry caught a two-year-old flounder whose length had a z-score of −0.5. How long was this fish?

Source: Turkish Journal of Veterinary and Animal Science, 29:1013–1018

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 3.3, Problem 21E

Chapter 3.3, Problem 23E

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Solution Summary: The author calculates the z -score for the given length, which is 1.33, and the length of the fish.

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