Question

listed below are amounts (in millions of dollars) collected from parking meters by a security company in a certain city. a larger data set was used to convict 5 members of the company of gr mean and median for each of the two samples and then compare the two sets of results. do the limited data listed here show evidence of stealing by the security companys employees? security company: 1.1 1.6 1.1 1.6 1.3 1.4 1.8 1.4 1.4 1.7 other companies: 1.9 2.3 2.1 1.6 2.1 1.7 2.3 1.6 1.6 1.5 a. the mean and the median for the security company are both lower than the mean and the median for the collections performed by other companies b. the median is lower for the collections performed by other companies, but the mean is lower for the security company c. the mean and median appear to be roughly the same for all collections d. the mean and the median for the collections performed by other companies are both lower than the mean and the median for the security company e. the mean is lower for the security company, but the median is lower for the collections performed by other companies do the limit data listed here show evidence of stealing by the security companys employees? a. since the security company does not appear to have collected lower revenue than the other companies, there is no evidence of stealing by the security companys employees b. since the security company appears to have collected lower revenue than the other companies, there is some evidence of stealing by the security companys employees c. the sample size is not large enough to show any meaningful results d. since the data is not matched, there is no evidence of stealing by the security companys employees

Explanation:

Step1: Calculate mean of security company

The sum of amounts for security company is $1.1 + 1.6+1.1+1.6+1.3+1.4+1.8+1.4+1.4+1.7 = 14.4$. There are $n = 10$ data - points. The mean $\bar{x}_1=\frac{14.4}{10}=1.44$.

Step2: Calculate median of security company

Arrange data in ascending order: $1.1,1.1,1.3,1.4,1.4,1.4,1.6,1.6,1.7,1.8$. Since $n = 10$ (even), the median $M_1=\frac{1.4 + 1.4}{2}=1.4$.

Step3: Calculate mean of other companies

The sum of amounts for other companies is $1.9+2.3+2.1+1.6+2.1+1.7+2.3+1.6+1.6+1.5 = 18.7$. There are $n = 10$ data - points. The mean $\bar{x}_2=\frac{18.7}{10}=1.87$.

Step4: Calculate median of other companies

Arrange data in ascending order: $1.5,1.6,1.6,1.6,1.7,1.9,2.1,2.1,2.3,2.3$. Since $n = 10$ (even), the median $M_2=\frac{1.7 + 1.9}{2}=1.8$.

Step5: Compare mean and median

We have $\bar{x}_1 = 1.44<\bar{x}_2=1.87$ and $M_1 = 1.4

Step6: Analyze evidence of stealing

Since the security company appears to have collected lower revenue (both in terms of mean and median) than the other companies, there is some evidence of stealing by the security company's employees.

Answer:

A. The mean and the median for the security company are both lower than the mean and the median for the collections performed by other companies
B. Since the security company appears to have collected lower revenue than the other companies, there is some evidence of stealing by the security company's employees