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Consider the following sets of sample data: A: 20,529, 22,081, 21,454, 21,449, 21,801, 21,892, 20,913, 20,075, 21,694, 21,681, 21,416, 21,829, 21,013, 22,053 B: 4.02, 4.71, 3.87, 4.57, 4.29, 4.49, 3.23, 2.94, 4.41, 3.07, 3.23 Step 1 of 2 : For each of the above sets of sample data, calculate the coefficient of variation, CV. Round to one decimal place.

Respuesta :

Answer:

Coefficient of Variation of Data A = 2.8%

Coefficient of Variation of Data B = 15.4%

Step-by-step explanation:

Coefficient of variation, CV formula is given by;

                 CV = [tex]\frac{Standard Deviation}{Mean} * 100[/tex]

  • Now CV of data sample A :

Firstly arranging data set A in ascending order we get,

20,075, 20,529, 20,913, 21,013, 21,416, 21,454, 21,449, 21,681, 21,694, 21,801, 21,829, 21,892, 22,053, 22,081

Mean of above data, Abar = [tex]\frac{\sum A_i}{n}[/tex] =

[tex]\frac{20,075+ 20,529+ 20,913+ 21,013+ 21,416+ 21,454+ 21,449+ 21,681+ 21,694+ 21,801+ 21,829+ 21,892+ 22,053+ 22,081}{14}[/tex]       Abar = 21420

Standard deviation of above data, [tex]S_A[/tex] = [tex]\frac{\sum (A_i - Abar)}{n-1}[/tex] = 591.2

So, Coefficient of Variation of data A, [tex]CV_A[/tex] = [tex]\frac{S_A}{Abar}*100[/tex]

                                                                      = [tex]\frac{591.2}{21420}*100[/tex] = 2.8%

  • Now CV for data sample B;

Arranging data set B in ascending order we get,

2.94, 3.07, 3.23, 3.23, 3.87, 4.02, 4.29, 4.41, 4.49, 4.57, 4.71

Mean of above data, Bbar = [tex]\frac{\sum B_i}{n}[/tex] =

[tex]\frac{2.94+ 3.07+ 3.23+ 3.23+ 3.87+ 4.02+ 4.29+ 4.41+ 4.49+ 4.57+4.71}{11}[/tex] = 3.9

Standard deviation of above data, [tex]S_B[/tex] = [tex]\frac{\sum (B_i - Bbar)}{n-1}[/tex] = 0.6

So, Coefficient of Variation of data B, [tex]CV_B[/tex] = [tex]\frac{S_B}{Bbar}*100[/tex]

                                                                      = [tex]\frac{0.6}{3.9}*100[/tex] = 15.4% .

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