Beginning Statistics, 2nd Edition
Beginning Statistics, 2nd Edition
2nd Edition
ISBN: 9781932628678
Author: Carolyn Warren; Kimberly Denley; Emily Atchley
Publisher: Hawkes Learning Systems
Question
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Chapter 3.2, Problem 22E
To determine

To find:

The coefficient of variation, CV, for each data set and the larger spread relative to its own mean between the given data sets.

Expert Solution & Answer
Check Mark

Answer to Problem 22E

Solution:

The coefficient of variation, CV, for data set A and B are 20.66% and 35.28% respectively. The data set corresponding to B has the larger spread relative to its own mean.

Explanation of Solution

Given information:

Given set of data set are,

A:31,33,35,39,31,32,30,40,13,41,38,32,37,33B:2.3,3.5,4.3,2.1,4.8,3.9,2.0,3.3,4.0,1.6,2.2

Formula used:

The formula to calculate the sample standard deviation for given set of data is,

s=(xix¯)2n1

Where, xi is the ith data value, x¯ is the sample mean, and N is the total number of collection.

The formula to calculate the coefficient of variance of a sample is,

C.V=sx¯×100%

x¯ is the sample mean and s is the sample standard deviation.

Calculation:

For data set A, nA=14, Compute x¯A for the given set of data,

xA¯=31+33+35+39+31+32+30+40+13+41+38+32+37+3314=46514=33.2143

Construct the table for sample standard deviation of the given set of data.

xiA xiAxA¯ (xiAxA¯)2
31 3133.2143=2.2143 4.90312449
33 3333.2143=0.2143 0.04592449
35 3533.2143=1.7857 3.18872449
39 3933.2143=5.7857 33.47432449
31 3133.2143=2.2143 4.90312449
32 3233.2143=1.2143 1.47452449
30 3033.2143=3.2143 10.33172449
40 4033.2143=6.7857 46.04572449
13 1333.2143=20.2143 408.61792449
41 4133.2143=7.7857 60.61712449
38 3833.2143=4.7857 22.90292449
32 3233.2143=1.2143 1.47452449
37 3733.2143=3.7857 14.33152449
33 3333.2143=0.2143 0.04592449
(xiAxA¯)2=612.3571

Substitute 612.3571 for (xiAxA¯)2 and 14 for nA in the formula of the standard deviation.

sA=(xiAxA¯)2nA1=612.357113=47.10446.8633

The sample standard deviation for the data set A is 6.8633.

Substitute 6.8633 for SA, and 33.2143 for xA¯ in the formula of coefficient of variance.

C.VA=sAxA¯×100%=6.863333.2143×100%=20.66%

The coefficient of variance for data set A is 20.66%.

For data set B, nB=11, Compute x¯B for the given set of data,

xB¯=2.3+3.5+4.3+2.1+4.8+3.9+2+3.3+4+1.6+2.211=3411=3.0909

Construct the table for sample standard deviation of the given set of data.

xiB xiBxB¯ (xiBxB¯)2
2.3 2.33.0909=0.7909 0.62552281
3.3 3.33.0909=0.2091 0.04372281
4.3 4.33.0909=1.2091 1.46192281
2.1 2.13.0909=0.9909 0.98188281
4.8 4.83.0909=1.7091 2.92102281
3.9 3.93.0909=0.8091 0.65464281
2.0 2.03.0909=1.0909 1.19006281
3.3 3.33.0909=0.2091 0.04372281
4.0 4.03.0909=0.9091 0.82646281
1.6 1.63.0909=1.4909 2.22278281
2.2 2.23.0909=0.8909 0.79370281
(xiBxB¯)2=11.8891

Substitute 11.8891 for (xiBxB¯)2 and 11 for nB in the formula of the standard deviation.

sB=(xiBxB¯)2nB1=11.889110=1.188911.0904

The sample standard deviation for the data set B is 1.0904.

Substitute 1.0904 for SB, and 3.0909 for xB¯ in the formula of coefficient of variance.

C.VB=sBxB¯×100%=1.09043.0909×100%35.28%

The coefficient of variance for data set B is 35.28%.

Coefficient of variance for sample B is greater than coefficient of variance for sample A.

C.VB>C.VA

The data set B has larger spread relative to its own mean.

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Chapter 3 Solutions

Beginning Statistics, 2nd Edition

Ch. 3.1 - Prob. 11ECh. 3.1 - Prob. 12ECh. 3.1 - Prob. 13ECh. 3.1 - Prob. 14ECh. 3.1 - Prob. 15ECh. 3.1 - Prob. 16ECh. 3.1 - Prob. 17ECh. 3.1 - Prob. 18ECh. 3.1 - Prob. 19ECh. 3.1 - Prob. 20ECh. 3.1 - Prob. 21ECh. 3.1 - Prob. 22ECh. 3.1 - Prob. 23ECh. 3.1 - Prob. 24ECh. 3.1 - Prob. 25ECh. 3.1 - Prob. 26ECh. 3.1 - Prob. 27ECh. 3.1 - Prob. 28ECh. 3.1 - Prob. 29ECh. 3.1 - Prob. 30ECh. 3.1 - Prob. 31ECh. 3.1 - Prob. 32ECh. 3.1 - Prob. 33ECh. 3.1 - Prob. 34ECh. 3.2 - Prob. 1ECh. 3.2 - Prob. 2ECh. 3.2 - Prob. 3ECh. 3.2 - Prob. 4ECh. 3.2 - Prob. 5ECh. 3.2 - Prob. 6ECh. 3.2 - Prob. 7ECh. 3.2 - Prob. 8ECh. 3.2 - Prob. 9ECh. 3.2 - Prob. 10ECh. 3.2 - Prob. 11ECh. 3.2 - Prob. 12ECh. 3.2 - Prob. 13ECh. 3.2 - Prob. 14ECh. 3.2 - Prob. 15ECh. 3.2 - Prob. 16ECh. 3.2 - Prob. 17ECh. 3.2 - Prob. 18ECh. 3.2 - Prob. 19ECh. 3.2 - Prob. 20ECh. 3.2 - Prob. 21ECh. 3.2 - Prob. 22ECh. 3.2 - Prob. 23ECh. 3.2 - Prob. 24ECh. 3.2 - Prob. 25ECh. 3.2 - Prob. 26ECh. 3.2 - Prob. 27ECh. 3.2 - Prob. 28ECh. 3.2 - Prob. 29ECh. 3.2 - Prob. 30ECh. 3.2 - Prob. 31ECh. 3.2 - Prob. 32ECh. 3.2 - Prob. 33ECh. 3.2 - Prob. 34ECh. 3.2 - Prob. 35ECh. 3.2 - Prob. 36ECh. 3.2 - Prob. 37ECh. 3.3 - Prob. 1ECh. 3.3 - Prob. 2ECh. 3.3 - Prob. 3ECh. 3.3 - Prob. 4ECh. 3.3 - Prob. 5ECh. 3.3 - Prob. 6ECh. 3.3 - Prob. 7ECh. 3.3 - Prob. 8ECh. 3.3 - Prob. 9ECh. 3.3 - Prob. 10ECh. 3.3 - Prob. 11ECh. 3.3 - Prob. 12ECh. 3.3 - Prob. 13ECh. 3.3 - Prob. 14ECh. 3.3 - Prob. 15ECh. 3.3 - Prob. 16ECh. 3.3 - Prob. 17ECh. 3.3 - Prob. 18ECh. 3.3 - Prob. 19ECh. 3.3 - Prob. 20ECh. 3.3 - Prob. 21ECh. 3.3 - Prob. 22ECh. 3.3 - Prob. 23ECh. 3.3 - Prob. 24ECh. 3.3 - Prob. 25ECh. 3.3 - Prob. 26ECh. 3.3 - Prob. 27ECh. 3.3 - Prob. 28ECh. 3.3 - Prob. 29ECh. 3.3 - Prob. 30ECh. 3.3 - Prob. 31ECh. 3.CR - Prob. 1CRCh. 3.CR - Prob. 2CRCh. 3.CR - Prob. 3CRCh. 3.CR - Prob. 4CRCh. 3.CR - Prob. 5CRCh. 3.CR - Prob. 6CRCh. 3.CR - Prob. 7CRCh. 3.CR - Prob. 8CRCh. 3.CR - Prob. 9CRCh. 3.CR - Prob. 10CRCh. 3.CR - Prob. 11CRCh. 3.CR - Prob. 12CRCh. 3.CR - Prob. 13CRCh. 3.CR - Prob. 14CRCh. 3.CR - Prob. 15CRCh. 3.PA - Prob. 1PCh. 3.PA - Prob. 2PCh. 3.PA - Prob. 3PCh. 3.PA - Prob. 4PCh. 3.PA - Prob. 5PCh. 3.PA - Prob. 6PCh. 3.PA - Prob. 7PCh. 3.PA - Prob. 8PCh. 3.PA - Prob. 9PCh. 3.PA - Prob. 10PCh. 3.PB - Prob. 1PCh. 3.PB - Prob. 2PCh. 3.PB - Prob. 3PCh. 3.PB - Prob. 4P
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