Answered: a) According to Tchebychev's…

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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a) According to Tchebychev's inequality, what is the minimum percentage of the data within k = 2 standard deviations of the mean?

within 2.5 standard deviations?

within 4 standard deviations?

b) For data within k=2 standard deviations, what is the difference between the empirical rule for mound shaped (normally distributed data) and the estimates of Tchebychev's inequality for irregularly shaped data?

c) Assume that an unknown distribution may be fairly irregular. Apply the Tchebychev inequality to determine the number, k, of standard deviations within the mean to guarantee at least each of the following percentages of the data:

at least 95% of the data?, at least 68% of the data?, at least 80% of the data?)

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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