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:
	
1.5
1.6
1.5
1.6
1.8
1.3
1.7
1.3
1.3
1.2
 
Other​ Companies:
	
1.6
1.8
1.9
2.3
1.9
1.5
1.8
2.3
2.3
2.2
Question content area bottom
Part 1
Find the means. 
The mean for the security company is ​$enter your response here
 
million and the mean for the other companies is ​$enter your response here
 
million.
​(Type integers or decimals rounded to two decimal places as​ needed.)

To find the mean (average) for both the security company and other companies, we use the following formula:

\[
\text{Mean} = \frac{\text{Sum of all data values}}{\text{Number of data values}}
\]

### 1. For the Security Company:
The data values are:  
1.5, 1.6, 1.5, 1.6, 1.8, 1.3, 1.7, 1.3, 1.3, 1.2

- First, sum these values:  
\[
1.5 + 1.6 + 1.5 + 1.6 + 1.8 + 1.3 + 1.7 + 1.3 + 1.3 + 1.2 = 14.8
\]

- There are 10 values, so the mean is:  
\[
\text{Mean for Security Company} = \frac{14.8}{10} = 1.48
\]

### 2. For the Other Companies:
The data values are:  
1.6, 1.8, 1.9, 2.3, 1.9, 1.5, 1.8, 2.3, 2.3, 2.2

- First, sum these values:  
\[
1.6 + 1.8 + 1.9 + 2.3 + 1.9 + 1.5 + 1.8 + 2.3 + 2.3 + 2.2 = 19.6
\]

- There are 10 values, so the mean is:  
\[
\text{Mean for Other Companies} = \frac{19.6}{10} = 1.96
\]

### Means:
- Mean for Security Company: **$1.48 million**
- Mean for Other Companies: **$1.96 million**

Now that we have calculated the means, we can see that the average amount collected by the security company is lower than that of other companies.

Would you like the details for the median or have any questions so far? Below are 5 related questions to expand understanding:

1. How do we calculate the median of a dataset?
2. Why is the median a useful measure in comparing data sets?
3. What does the lower mean for the security company suggest about the data?
4. How might outliers affect the mean in both data sets?
5. How would you verify if the data shows evidence of theft or irregularities?

**Tip:** Always double-check the number of data points before calculating averages or other statistics to avoid miscalculations.

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:
1.5, 1.6, 1.5, 1.6, 1.8, 1.3, 1.7, 1.3, 1.3, 1.2

Other Companies:
1.6, 1.8, 1.9, 2.3, 1.9, 1.5, 1.8, 2.3, 2.3, 2.2


Learn how to calculate the mean and median of parking meter collections for a security company and compare them with other companies. This problem provides a detailed comparison and asks if the data shows evidence of theft. Suitable for Grades 9-12 students learning statistics.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation