Answered: (a) The population 3, 4, 9, 14, and 20…

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) The population 3, 4, 9, 14, and 20 has a mean of 10 and a standard deviation of 6.356. The z-scores for each of the five data values are

z₃ ≈ −1.101,

z₄ ≈ −0.944,

z₉ ≈ −0.157,

z₁₄ ≈ 0.629,

and z₂₀ ≈ 1.573.

Find the mean and the standard deviation of these z-scores.

mean
standard deviation

(b) The population 2, 6, 12, 17, 22, and 25 has a mean of 14 and a standard deviation of 8.226. The z-scores for each of the six data values are

z₂ ≈ −1.459,

z₆ ≈ −0.973,

z₁₂ ≈ −0.243,

z₁₇ ≈ 0.365,

z₂₂ ≈ 0.973,

and z₂₅ ≈ 1.337.

Find the mean and the standard deviation of these z-scores.

mean
standard deviation

(c) Use the results of part (a) and part (b) to make a conjecture about the mean and standard deviation of the z-scores for any set of data.

The mean of the z-scores is always 1, and their standard deviation is 0.

The mean of the z-scores is always 1 more than the standard deviation.

The mean and standard deviation of z-scores are never the same.

The mean of the z-scores is always 0, and their standard deviation is 1.

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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