Answered: A random sample of 25 U.S. residents…

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 random sample of 25 U.S. residents was selected using census data from the year 2000. The dotplot below shows the distribution of total personal income (in thousands) for the members of the sample. The mean of this distribution is $25,615 and the standard deviation is $25,333. (a) Calculate and interpret the percentile for the individual with a total personal income of $35,000. Show work. (b) Calculate and interpret the z-score for the individual who had a total personal income of $10,000. Show work.

Sample of Collection 1
܀܀
20
0
40
60
80
Total personal income (thousands)
100
Dot Plot
120

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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