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 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 company’s 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
the median for the security company is $ 1.45 million and the median for the other companies is $ 1.95 million. (type integers or decimals rounded to two decimal places as needed.)
compare the results. choose the correct answer below.
a. the mean and median appear to be roughly the same for all collections.
b. 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. 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 collections performed by other companies are both lower than the mean and the median for the security company.
e. the median is lower for the collections performed by other companies, but the mean is lower for the security company.

Explanation:

Step1: Calculate the mean for the security company

The sum of the security - company values is \(1.6 + 1.7+1.6 + 1.7+1.2+1.4+1.3+1.4+1.4+1.5 = 14.8\). There are \(n = 10\) values. The mean \(\bar{x}_1=\frac{14.8}{10}=1.48\).

Step2: Calculate the mean for other companies

The sum of the other - companies values is \(1.6+2.2 + 2.1+1.8+2.1+1.7+2.2+1.8+1.8+2.3=19.6\). There are \(n = 10\) values. The mean \(\bar{x}_2=\frac{19.6}{10}=1.96\).

Step3: Analyze the comparison

We know the median for the security company is \(1.45\) and for other companies is \(1.95\). The mean for the security company (\(1.48\)) and median (\(1.45\)) are both lower than the mean (\(1.96\)) and median (\(1.95\)) for other companies.

Answer:

B. 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.