A16. Height (om)2179317441561716.17071658.17015710155111571217713172141541515516158171701817419170201542117222164231732416425172261732715028150291603015031166 e. Calculate Variance, Standard deviation, and Coefficient of Variation (CV) of the student's heights.

Name: A16. Height (om)2179317441561716.17071658.170157101551115712177131721
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Description: A16. Height (om)2179317441561716.17071658.17015710155111571217713172141541515516158171701817419170201542117222164231732416425172261732715028150291603015031166 e. Calculate Variance, Standard deviation, and Coefficient of Variation (CV) of the studen

Let X be the height of the student. A 179 174 156 171 170 165 170 157 155…

Answered: Calculate Variance, Standard deviation,…

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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A
1
6. Height (om)
2
179
3
174
4
156
171
6.
170
7
165
8.
170
157
10
155
11
157
12
177
13
172
14
154
15
155
16
158
17
170
18
174
19
170
20
154
21
172
22
164
23
173
24
164
25
172
26
173
27
150
28
150
29
160
30
150
31
166

e. Calculate Variance, Standard deviation, and Coefficient of Variation (CV) of the student's heights.

Expert Solution

Step 1

Let X be the height of the student.

A
179
174
156
171
170
165
170
157
155
157
177
172
154
155
158
170
174
170
154
172
164
173
164
172
173
150
150
160
150
166

It is required to obtained the variance, standard deviation, and coefficient of variance.

Step 2

The formula for variance (σ²) is

$σ^{2} = \frac{\sum_{}^{} {(X - \bar{X})}^{2}}{N - 1}$
where

$\bar{X} = \frac{\sum_{}^{} X}{N}$

$\bar{X} = \frac{4932}{30}$

$\bar{X} = 164.4$

Therefore,

X	$(X - \bar{X})$	$\sum_{}^{} {(X - \bar{X})}^{2}$
179	14.6	213.16
174	9.6	92.16
156	-8.4	70.56
171	6.6	43.56
170	5.6	31.36
165	0.6	0.36
170	5.6	31.36
157	-7.4	54.76
155	-9.4	88.36
157	-7.4	54.76
177	12.6	158.76
172	7.6	57.76
154	-10.4	108.16
155	-9.4	88.36
158	-6.4	40.96
170	5.6	31.36
174	9.6	92.16
170	5.6	31.36
154	-10.4	108.16
172	7.6	57.76
164	-0.4	0.16
173	8.6	73.96
164	-0.4	0.16
172	7.6	57.76
173	8.6	73.96
150	-14.4	207.36
150	-14.4	207.36
160	-4.4	19.36
150	-14.4	207.36
166	1.6	2.56

$σ^{2} = \frac{\sum_{}^{} {(X - \bar{X})}^{2}}{N - 1}$

= $\frac{2305.2}{30}$

= 79.48966

The variance of students heights is 79.48966

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