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: 1.6 1.7 1.6 1.7 1.2 1.4 1.3 1.4 1.4 1.5 other companies: 1.6 2.2 2.1 1.8 2.1 1.7 2.2 1.8 1.8 2.3 do the limit data listed here show evidence of stealing by the security companys employees? a. 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. b. the sample size is not large enough to show any meaningful results. c. since the data is not matched, there is no 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 mean of security company
The mean $\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}$. For the security - company data set $x={1.6,1.7,1.6,1.7,1.2,1.4,1.3,1.4,1.4,1.5}$, $n = 10$, and $\sum_{i=1}^{10}x_{i}=1.6 + 1.7+1.6+1.7+1.2+1.4+1.3+1.4+1.4+1.5 = 14.2$. So, $\bar{x}_{security}=\frac{14.2}{10}=1.42$.
Step2: Calculate median of security company
First, order the data set: $1.2,1.3,1.4,1.4,1.4,1.5,1.6,1.6,1.7,1.7$. Since $n = 10$ (even), the median $M=\frac{\frac{n}{2}^{th}\text{ value}+\left(\frac{n}{2}+1\right)^{th}\text{ value}}{2}=\frac{1.4 + 1.5}{2}=1.45$.
Step3: Calculate mean of other companies
For the other - companies data set $x={1.6,2.2,2.1,1.8,2.1,1.7,2.2,1.8,1.8,2.3}$, $n = 10$, and $\sum_{i = 1}^{10}x_{i}=1.6+2.2+2.1+1.8+2.1+1.7+2.2+1.8+1.8+2.3 = 19.6$. So, $\bar{x}_{other}=\frac{19.6}{10}=1.96$.
Step4: Calculate median of other companies
Order the data set: $1.6,1.7,1.8,1.8,1.8,2.1,2.1,2.2,2.2,2.3$. Since $n = 10$ (even), the median $M=\frac{\frac{n}{2}^{th}\text{ value}+\left(\frac{n}{2}+1\right)^{th}\text{ value}}{2}=\frac{1.8 + 2.1}{2}=1.95$.
Step5: Compare means and medians
We have $\bar{x}{security}=1.42<\bar{x}{other}=1.96$ and $M_{security}=1.45<M_{other}=1.95$.
Step6: Determine evidence of stealing
Since the security company appears to have collected lower revenue (both mean and median are lower) than the other companies, there is some evidence of stealing by the security company's employees.
Answer:
The mean for the security company is $1.42$ million dollars and the median is $1.45$ million dollars. The mean for other companies is $1.96$ million dollars and the median is $1.95$ million dollars. The mean and the median for the collections performed by other companies are both higher than the mean and the median for the security company. A. 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.