Answered: The owners of a manufacturing company…

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 owners of a manufacturing company conducted a survey to determine the mean income of the customers who prefer the company’s brand of clothing. From a random sample of 100 customers, it was determined that their mean income was $47,600. Which conclusion can be made based on this information?

Select one:

1. The total population mean cannot be determined by such a small random sample.

2. The total population mean must be close to $47,600 based on statistical inference.

3. The total population mean must be much greater than $47,600 because there are more people in the total population.

4. The total population mean must be much less than $47,600 because, out of a sample of 100, a few people with a very high mean income would skew 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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