listed below are amounts (in millions of dollars) collected from parking meters by a security company in a…

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 grand larceny. find the 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: 15 13 15 13 11 12 16 12 12 14 other companies: 18 21 17 22 17 19 21 22 22 16 a. the median is lower for the collections performed by other companies, but the mean is lower for the security company b. the mean and median appear to be roughly the same for all collections c. the mean is lower for the security company, but the median is lower for the collections performed by other companies d. 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 e. 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 do the limit data listed here show evidence of stealing by the security companys employees? a. since the data is not matched, there is no evidence of stealing by the security companys employees b. the sample size is not large enough to show any meaningful results. c. 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 d. 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

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 grand larceny. find the 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: 15 13 15 13 11 12 16 12 12 14 other companies: 18 21 17 22 17 19 21 22 22 16 a. the median is lower for the collections performed by other companies, but the mean is lower for the security company b. the mean and median appear to be roughly the same for all collections c. the mean is lower for the security company, but the median is lower for the collections performed by other companies d. 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 e. 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 do the limit data listed here show evidence of stealing by the security companys employees? a. since the data is not matched, there is no evidence of stealing by the security companys employees b. the sample size is not large enough to show any meaningful results. c. 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 d. 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

Answer

Explanation:

Step1: Calculate the mean for the security company

The formula for the mean $\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}$. For the security company, $x = [15,13,15,13,11,12,16,12,12,14]$, $n = 10$. $\sum_{i=1}^{10}x_{i}=15 + 13+15+13+11+12+16+12+12+14 = 133$. So the mean $\bar{x}_{1}=\frac{133}{10}=13.3$.

Step2: Calculate the median for the security company

First, order the data: $[11,12,12,12,13,13,14,15,15,16]$. Since $n = 10$ (even), the median is the average of the $\frac{n}{2}$ - th and $(\frac{n}{2}+1)$ - th ordered values. The 5 - th value is 13 and the 6 - th value is 13, so the median $M_{1}=\frac{13 + 13}{2}=13$.

Step3: Calculate the mean for other companies

For other companies, $x=[18,21,17,22,17,19,21,22,22,16]$, $n = 10$. $\sum_{i = 1}^{10}x_{i}=18+21+17+22+17+19+21+22+22+16=195$. So the mean $\bar{x}_{2}=\frac{195}{10}=19.5$.

Step4: Calculate the median for other companies

Order the data: $[16,17,17,18,19,21,21,22,22,22]$. Since $n = 10$ (even), the 5 - th value is 19 and the 6 - th value is 21, so the median $M_{2}=\frac{19 + 21}{2}=20$.

Step5: Compare the results

We have $\bar{x}{1}=13.3<\bar{x}{2}=19.5$ and $M_{1}=13<M_{2}=20$. The mean and median for the security company are both lower than those for other companies.

Step6: Analyze the evidence of stealing

Since the security company has lower mean and median amounts collected compared to other companies, there is some evidence of stealing by the security - company's employees.

Answer:

D. 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. C. 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.