Answered: a)Determine the mean of sample means…

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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Question

a)Determine the mean of sample means distribution
b) Determine the standard deviation (standard error) of sample means distribution
c) Draw a Normal (bell-shaped) graph for sample means distribution by
hand on a paper showing x and y axes without any values marked on them. However,
label the values of mean and standard deviation as described below.

The adult male heights in a country vary normally with mean of 70 inches and standard
deviation of 4 inches. We draw many samples of size 100 from the above population
using repeated random sampling and record the mean height for each sample to constitute
a sample means distribution (?̅ -distribution). Do the above for the distribution.

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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