Question

Consider the following sets of sample data: A: $30,600, $29,900, $37,500, $29,200, $25,100, $37,400, $26,100, $35,400, $31,500, $34,600, $33,200, $23,100, $25,200, $38,000

B: 89, 78, 85, 81, 76, 97, 70, 73, 88, 76, 99

Step 1 of 2: For each of the above sets of sample data, calculate the coefficient of variation, CV. Round to one decimal place.

CV FOR DATA SET A:

CV FOR DATA SET B:

Step 2 of 2:

Which of the above sets of sample data has the smaller spread?

Answer 1

Solution

A )Given that

x	x2
30600	936360000
29900	894010000
37500	1406250000
29200	852640000
25100	630010000
37400	1398760000
26100	681210000
35400	1253160000
31500	992250000
34600	1197160000
33200	1102240000
23100	533610000
25200	635040000
38000	1444000000
x=436800	x2=13956700000

The sample mean is

Mean = (x / n) )

=30600+29900+37500+29200+25100+37400+26100+35400+31500+34600+33200+23100+25200+38000 /14

=436800 /14

=31200

The sample standard is S

  S =( x² ) - (( x)² / n ) n -1

=13956700000-(436800)21413

=13956700000-1362816000013

=32854000013

=25272307.6923

=5027.157

Co-efficient of Variation (Sample) =S / ⋅100%

=5027.157 / 31200⋅100%

=16.11%

Co-efficient of Variation = 16.1%

B ) Given that

x	x2
89	7921
78	6084
85	7225
81	6561
76	5776
97	9409
70	4900
73	5329
88	7744
76	5776
99	9801
x=912	x2=76526

The sample mean is

Mean = (x / n) )

=89+78+85+81+76+97+70+73+88+76+99 /11

=912/11

The sample standard is S

  S =( x² ) - (( x)² / n ) n -1

=76526-(912)²11 /10

=76526-75613.0909/10

=912.9091/10

=91.2909

=9.5546

Co-efficient of Variation (Sample) =S/ ⋅100%

=9.5546 /82.9091⋅100%

=11.52%

Co-efficient of Variation = 11.5%

B sets is the above sets of sample data has the smaller spread