Answered: The population (N = 3) consists of…

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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The population (N = 3) consists of three children whose ages are 4, 5, and 9; the following Questions pertains to the age of the children. Assume that samples of size n = 2 are randomly selected with replacement.

A. Find the value of the population standard deviation s.

B. Table 6-2 describes the sampling distribution of the sample mean. Construct a similar table representing the sampling distribution at the sample standard deviation S. Then combine values of S that are the same as in table 6-3.

C. Find the mean of the sampling distribution of the sample standard deviation.

D. Based on the preceding results, is the sample standard deviation an unbiased estimator at the population standard deviation? Why or why not?

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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