Question

Consider the following sets of sample data:

A:

21,963

, 20,786, 21,202, 22,251, 21,848, 20,431, 20,336, 22,017, 20,119, 21,984, 20,261, 20,570, 20,855, 21,971

B:

86

, 74, 92, 73, 74, 83, 80, 91, 76, 99, 72

Step 1 of 2 :

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

Answer 1

Solution:

a ) Given that

x	x2
21963	482373369
20786	432057796
21202	449524804
22251	495107001
21848	477335104
20431	417425761
20336	413552896
22017	484748289
20119	404774161
21984	483296256
20261	410508121
20570	423124900
20855	434931025
21971	482724841
∑x=296594	∑x2=6291484324

The sample mean is $\bar x$

Mean $\bar x$ = ($\sum$x / n) )

=21963+20786+21202+22251+21848+20431+20336+22017+20119+21984+20261+20570+20855+21971 /14

=296594 /14

=21185.285

Mean $\bar x$ =21185.285

The sample standard is S

  S =$\sqrt{}$( $\sum$ x² ) - (( $\sum$ x)² / n ) n -1

=$\sqrt{}$6291484324-(296594)²14 /13

=$\sqrt{}$6291484324-6283428631.1429 /13

=$\sqrt{}$8055692.8571/13

=$\sqrt{}$619668.6813

=787.1904

he sample standard is =787.1904

Co-efficient of Variation (Sample) = Sˉ / $\bar x$ *100%

=( 787.1904 / 21185.2857) *100%

=3.72%

Co-efficient of Variation (Sample) = 3.7%

b ) Given that

x	x2
86	7396
74	5476
92	8464
73	5329
74	5476
83	6889
80	6400
91	8281
76	5776
99	9801
72	5184
∑x=900	∑x2=74472

Solution

The sample mean is $\bar x$

Mean $\bar x$ = ($\sum$x / n) )

=86+74+92+73+74+83+80+91+76+99+72 /11

=900 /11

=81.8182

The sample standard is S

  S =$\sqrt{}$( $\sum$ x² ) - (( $\sum$ x)² / n ) n -1

=$\sqrt{}$74472-(900)²11 /10

=$\sqrt{}$74472-73636.3636/10

=$\sqrt{}$835.6364/10

=$\sqrt{}$83.5636

=9.1413

Co-efficient of Variation (Sample) = S / $\bar x$ *100%

=9.141381.8182⋅100%

=11.17%

Co-efficient of Variation (Sample) =11.2%