Question

Given Samples A and B below,

Sample A:	2.4	3.4	4.8	4.5	3.1	4.5	4.5	2.4	2.0
Sample B:	3.0	3.9	4.3	3.7	3.9	3.4	4.2	4.9	3.4

a. Calculate the mean and standard deviation for each sample.

Sample A:  x̄  A = x̄  A =

  ; s A = ; s A =

Sample B:  x̄  B = x̄  B =

  ; s B = ; s B =

Round to two decimal places if necessary

b. Calculate the coefficient of variation for each sample.

Sample A: CV A =CV A =

%

Sample B: CV B =CV B =

%

Round to two decimal places if necessary

c. Which sample is more variable?

Sample A

Sample B

Neither sample is more variable than the other

please show all steps im having trouble with S2A and S2B the most in the first part

Answer 1

Solution:

a) SAMPLE A:

Mean = (2.4 + 3.4 + 4.8 + 4.5 + 3.1 + 4.5 + 4.5 + 2.4 + 2.0)/9
= 31.6/9
Mean = 3.5111

Standard Deviation σ = √(1/9 - 1) x ((2.4 - 3.5111)2 + (3.4 - 3.5111)2 + (4.8 - 3.5111)2 + (4.5 - 3.5111)2 + (3.1 - 3.5111)2 + (4.5 - 3.5111)2 + (4.5 - 3.5111)2 + (2.4 - 3.5111)2 + (2.0 - 3.5111)2)
= √(1/8) x ((-1.1111)2 + (-0.1111)2 + (1.2889)2 + (0.9889)2 + (-0.4111)2 + (0.9889)2 + (0.9889)2 + (-1.1111)2 + (-1.5111)2)
= √(0.125) x ((1.23454321) + (0.01234321) + (1.66126321) + (0.97792321) + (0.16900321) + (0.97792321) + (0.97792321) + (1.23454321) + (2.28342321))
= √(0.125) x (9.52888889)
= √(1.19111111125)
= 1.0914

SAMPLE B

Mean = (3.0 + 3.9 + 4.3 + 3.7 + 3.9 + 3.4 + 4.2 + 4.9 + 3.4)/9
= 34.7/9
Mean = 3.8556

Standard Deviation σ = √(1/9 - 1) x ((3.0 - 3.8556)2 + (3.9 - 3.8556)2 + (4.3 - 3.8556)2 + (3.7 - 3.8556)2 + (3.9 - 3.8556)2 + (3.4 - 3.8556)2 + (4.2 - 3.8556)2 + (4.9 - 3.8556)2 + (3.4 - 3.8556)2)
= √(1/8) x ((-0.8556)2 + (0.0444)2 + (0.4444)2 + (-0.1556)2 + (0.0444)2 + (-0.4556)2 + (0.3444)2 + (1.0444)2 + (-0.4556)2)
= √(0.125) x ((0.73205136) + (0.00197136) + (0.19749136) + (0.02421136) + (0.00197136) + (0.20757136) + (0.11861136) + (1.09077136) + (0.20757136))
= √(0.125) x (2.58222224)
= √(0.32277778)
= 0.5681

b) SAMPLE A

Cofficient of Varaiance =σ/μ
=1.0914/3.5111
Coefficient of Variance = 0.3108

SAMPLE B

Cofficient of Varaiance =σ/μ
=0.5681/3.8556
Coefficient of Variance = 0.1474

c) SAMPLE A is more variable

The sample A having more Coefficient of Variation so it will be more variable.