Question

isted below are amounts​ (in millions of​ dollars) collected from parking meters by a security service company and other companies during similar time periods. Do the limited data listed here show evidence of stealing by the security service​ company's employees? Security Service Company: 1.5 1.7 1.6 1.4 1.7 1.5 1.8 1.4 1.4 1.5 Other Companies: 1.8 1.9 1.6 1.7 1.8 1.9 1.6 1.5 1.7 1.8 Find the coefficient of variation for each of the two​ samples, then compare the variation. The coefficient of variation for the amount collected by the security service company is nothing​%. ​(Round to one decimal place as​ needed.)

Answer 1

Means:

1.55

1.73

Standard Deviation:

0.1434

0.1338

Coefficient of variation:

9.2

7.7

the limited data listed here shows evidence of stealing by the security service​ company's employees.

Explanation:

Given data:

security Service Company Other Companies

x₁ x₂

1.5 1.8

1.7 1.9

1.6 1.6

1.4 1.7

1.7 1.8

1.5 1.9

1.8 1.6

1.4 1.5

1.4 1.7

1.5 1.8

n₁ = 10 n₂ = 10

To find:

coefficient of variation for each of the two​ samples

Solution:

The formula for calculating coefficient of variation of sample is:

Coefficient of Variation (CV) = (Standard Deviation / Mean) * 100%

Calculate Mean for Security Service Company data:

Mean = (Σ x₁) / n₁

= (1.5 + 1.7 + 1.6 + 1.4 + 1.7 + 1.5 + 1.8 + 1.4 + 1.4 + 1.5) / 10

= 15.5 / 10

Mean = 1.55

Calculate Standard Deviation for Security Service Company data:

Standard Deviation = √∑(x₁ - Mean)²/n₁-1

= √∑(1.5-1.55)² + (1.7-1.55)² + (1.6-1.55)² + (1.4-1.55)² + (1.7-1.55)² + (1.5-1.55)² + (1.8-1.55)² + (1.4-1.55)² + (1.4-1.55)² + (1.5-1.55)² / 10-1

=√∑ (−0.05)² + (0.15)² + (0.05)² + (−0.15)² + (0.15)² + (−0.05)² + (0.25)² + (−0.15)² + (−0.15)² + (−0.05)² / 10 - 1

= √∑0.0025 + 0.0225 + 0.0025 + 0.0225 + 0.0225 + 0.0025 + 0.0625 + 0.0225 + 0.0225 + 0.0025 / 9

= √0.185 / 9

= √0.020555555555556

= 0.14337208778404

= 0.143374

Standard Deviation = 0.143374

Coefficient of Variation for Security Service Company:

CV = (Standard Deviation / Mean) * 100%

= (0.143374 / 1.55) * 100

= 0.09249935 * 100

= 9.249935

CV = 9.2

CV = 9.2%

Calculate Mean for Other Companies data:

Mean = (Σ x₂) / n₂

= (1.8 + 1.9 + 1.6 + 1.7 + 1.8 + 1.9 + 1.6 + 1.5 + 1.7 + 1.8) / 10

= 17.3 / 10

Mean = 1.73

Calculate Standard Deviation for Other Companies data:

Standard Deviation = √∑(x₂-Mean)²/n₂-1

= √∑[(1.8-1.73)² + (1.9-1.73)² + (1.6-1.73)² + (1.7-1.73)² + (1.8-1.73)² + (1.9-1.73)² + (1.6-1.73)² + (1.5-1.73)² + (1.7-1.73)² + (1.8-1.73)²] / 10 - 1

= √∑ [(0.07)² + (0.17)² + (-0.13)² + (-0.03)² + (0.07)² + (0.17)² + (-0.13)² + (-0.23)² + (-0.03)² + (0.07)²] / 9

= √∑ (0.0049 + 0.0289 + 0.0169 + 0.0009 + 0.0049 + 0.0289 + 0.0169 + 0.0529 + 0.0009 + 0.0049) / 9

= √(0.161 / 9)

= √0.017888888888889

= 0.13374935098493

= 0.13375

Standard Deviation = 0.13375

Coefficient of Variation for Other Companies:

CV = (Standard Deviation / Mean) * 100%

= (0.13375 / 1.73) * 100

= 0.077312 * 100

= 7.7312

CV = 7.7

CV = 7.7%

Yes, the limited data listed here shows evidence of stealing by the security service​ company's employees because there is a significant difference in the variation.