Answered: Windy, part I To select the site for an…

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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Windy, part I To select the site for an electricity-
generating wind turbine, wind speeds were recorded at

several potential sites every 6 hours for a year. Two sites
not far from each other looked good. Each had a mean
wind speed high enough to qualify, but we should choose
the site with a higher average daily wind speed. Because
the sites are near each other and the wind speeds were
recorded at the same times, we should view the speeds aspaired. Here are the summaries of the speeds (in miles
per hour):

Is there a mistake in this output? Why doesn’t the
Pythagorean Theorem of Statistics work here? In other
words, shouldn’t
SD1site2 - site42 = 2SD2

1site22 + SD2
1site42?
But 213.58622 + 13.42122 = 4.956, not 2.551 as given
by the software. Explain why this happened.

Variable Count Mean StdDev
site2 1114 7.452 3.586
site4 1114 7.248 3.421
site2–site4 1114 0.204 2.551

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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