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 companies:
Security Company (#'s on left) Other Companies (#'s on right)
1.6; 1.5
1.8; 2.1
1.6; 1.9
1.8; 2.2
1.7; 1.9
1.2; 1.7
1.1; 2.1
1.2; 2.2
1.2; 2.2
1.5; 1.8
Find the means.
The mean for the security company is $ ___ million and the mean for the other companies is $ ____?
Find the medians.
The median for the security company is $ ___ million and the median for the other companies is $ ____?
Compare the results. Choose the correct answer below.
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 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 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.

Answer 1

Answer: B

Step-by-step explanation: To obtain the mean for a general set of data, the formula used is;

= (sum of all the data set)/ (number of data set)

The number of data set for the two samples is 10

For the mean for the security company;

= (1.6+1.8+1.6+1.8+1.7+1.2+1.1+1.2+1.2+1.5)/10 = 14.7/10

= $ 1.47million

For the mean for the other companies;

= (1.5+2.1+1.9+2.2+1.9+1.7+2.1+2.2+2.2+1.8)/10 =19.6/10

= $ 1.96 million

The data from the samples have to be rearranged before the median can be obtained;

For the Security Company;

1.1 1.2 1.2 1.2 1.5 1.6 1.6 1.7 1.8 1.8

There are two data sets in the middle, therefore the median will be obtained by finding the average of the data sets;

= (1.5+1.6)/2 =$ 1.55 million

For the other companies;

1.5 1.7 1.8 1.9 1.9 2.1 2.1 2.2 2.2 2.2

There are two data sets in the middle, therefore the median will be obtained by finding the average of the data sets;

= (1.9+2.1)/2 = $ 2.00 million

Therefore, the answer is B