Answered: Biologists and ecologists record the…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Biologists and ecologists record the distributions of measurements made on animal species to help study the distribution and evolution of the animals. The African ¯nch Pyrenestes ostrinus is interesting because the distribution of its bill size has two peaks even though other body measurements follow Normal distributions. For example, a study in Cameroon found that the wing length of male ¯nches varies according to a Normal distribution with mean 61.2 mm and standard deviation 1.8 mm.

(a) What proportion of male ¯nches have wings longer than 65 mm?

(b) What is the wing length that only 2% of male finches exceed?

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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