Consider the following summary statistics for two data sets: DATA ADATA BMean59.57.5Standard Deviation8.41.3 a. Compute the Coefficients of Variation for each sample. Round results to 1 decimal place.DATA ADATA B CVA= % CVB= % b. In which population, DATA A or DATA B, is the data more variable? c. Compute a 81 % Chebyshev's Theorem interval for DATA B:First find the corresponding value of kk for a 81 % interval. E.g, determine the value of kk (round to 1 decimal place) such that: 1−1k2= 0.81 k= Now construct the upper and lower bounds of the interval (round results to 1 decimal place). By Chebyshev's Theorem, at least 81 % of the data falls within the interval that is ±k±k standard deviations of the mean. So the interval is: to d. An intern computed the following Chebyshev’s theorem interval for DATA B: [5.6,9.5][5.6,9.5] What value of kk did the intern use, and what does it mean in the context of this interval? Give result to 1 decimal place. What is the minimum proportion of DATA B that is contained in the interval? Give result to nearest whole percent. %

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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

Consider the following summary statistics for two data sets:

	DATA A	DATA B
Mean	59.5	7.5
Standard Deviation	8.4	1.3

a. Compute the Coefficients of Variation for each sample. Round results to 1 decimal place.

DATA A	DATA B
CVA= %	CVB= %

b. In which population, DATA A or DATA B, is the data more variable?

c. Compute a 81 % Chebyshev's Theorem interval for DATA B:

First find the corresponding value of kk for a 81 % interval. E.g, determine the value of kk (round to 1 decimal place) such that:

1−1k2= 0.81 k=

Now construct the upper and lower bounds of the interval (round results to 1 decimal place). By Chebyshev's Theorem, at least 81 % of the data falls within the interval that is ±k±k standard deviations of the mean. So the interval is:

d. An intern computed the following Chebyshev’s theorem interval for DATA B:

[5.6,9.5][5.6,9.5]

What value of kk did the intern use, and what does it mean in the context of this interval? Give result to 1 decimal place.

What is the minimum proportion of DATA B that is contained in the interval? Give result to nearest whole percent.

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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