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Name: The coefficient of variation CV describes the standard deviation as a
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Description: The coefficient of variation CV describes the standard deviation as a percent of the mean. Because it has no units, you can use the coefficient of variation to compare data with different units. Find the coefficient of variation for each sample data

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

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Section: Chapter Questions

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The coefficient of variation CV describes the standard deviation as a percent of the mean. Because it has no units, you can use the coefficient of variation to compare data with different units. Find the coefficient of variation for each sample data set. What can you conclude?

CV = Standard deviation / Mean • 100%

Heights	Weights

65	198
65	210
66	220
67	226
80	168
74	184
74	179
71	221
69	181
65	187
76	230
72	168

CV heights = _______ %

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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Step 1

Given Information:

The coefficient of variation CV describes the standard deviation as a percent of the mean.

It is given by the formula:

$C V = \frac{s \tan d a r d d e v i a t i o n}{m e a n} \times 100 %$

To find the coefficient of variation for each sample data set:

First compute the mean and standard deviation for each sample:

Heights:

Mean is the sum of observations divided by the total no. of observations. It is calculated as follows:

$\begin{array}{rcl} \bar{x} & = & \frac{65 + 65 + 66 + 67 + 80 + 74 + 74 + 71 + 69 + 65 + 76 + 72}{12} \\ = & \frac{844}{12} \\ = & 70.33333333 \\ \approx & 70.3333 \end{array}$

Standard deviation is calculated using the formula:

$\begin{array}{rcl} s & = & \sqrt{\frac{\sum_{i} {(x_{i} - \bar{x})}^{2}}{n - 1}} \\ = & \sqrt{\frac{{(65 - 70.3333)}^{2} + {(65 - 70.3333)}^{2} + {(66 - 70.3333)}^{2} + . . . . . . {(72 - 70.3333)}^{2}}{12 - 1}} \\ \approx & 4.9787 \end{array}$

Substitute the values in the formula of Coefficient of variation:

$\begin{array}{rcl} C V & = & \frac{s \tan d a r d d e v i a t i o n}{m e a n} \times 100 % \\ = & \frac{4.9787}{70.3333} \times 100 % \\ = & 7.078723734 % \\ \approx & 7.08 % \end{array}$

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