Answered: The coefficient of variation CV…

Name: The coefficient of variation CV describes the standard deviation as a
Uploaded: 2024-03-20T07:06:16.000Z
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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

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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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 = _______ %

Expert Solution

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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