Question

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Part 1
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:
1.2
1.6
1.2
1.6
1.4
1.3
1.8
1.3
1.3
1.5

Other​ Companies:
1.5
1.7
2.2
2.3
2.2
1.8
1.7
2.3
2.3
1.6
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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.)

Answer 1

Explanation:

To find the mean for each data set, we need to sum up all the values and then divide by the total number of values.

For the Security Company data set:

Sum of values = 1.2 + 1.6 + 1.2 + 1.6 + 1.4 + 1.3 + 1.8 + 1.3 + 1.3 + 1.5 = 14.2

Number of values = 10

Mean = sum of values / number of values = 14.2 / 10 = 1.42 million dollars

For the Other Companies data set:

Sum of values = 1.5 + 1.7 + 2.2 + 2.3 + 2.2 + 1.8 + 1.7 + 2.3 + 2.3 + 1.6 = 19.6

Number of values = 10

Mean = sum of values / number of values = 19.6 / 10 = 1.96 million dollars

The mean for the Security Company data set is 1.42 million dollars and the mean for the Other Companies data set is 1.96 million dollars.

Part 2

Find the medians.

The median for the security company is $ enter your response here million and the median for the other companies is $ enter your response here million.

​(Type integers or decimals as​ needed.)

To find the median, we need to first arrange the values in order from smallest to largest.

For the Security Company data set:

1.2, 1.2, 1.3, 1.3, 1.4, 1.5, 1.6, 1.6, 1.8, 1.3

Since there are 10 values, the median is the average of the fifth and sixth values:

Median = (1.4 + 1.5) / 2 = 1.45 million dollars

For the Other Companies data set:

1.5, 1.6, 1.7, 1.7, 1.8, 2.2, 2.2, 2.3, 2.3, 2.3

Since there are 10 values, the median is the average of the fifth and sixth values:

Median = (1.8 + 2.2) / 2 = 2.0 million dollars

Part 3

Compare the mean and median for each sample. Do the limited data shown here indicate evidence of stealing by the security company's​ employees? Explain.

For the Security Company data set, the mean is 1.42 million dollars and the median is 1.45 million dollars. For the Other Companies data set, the mean is 1.96 million dollars and the median is 2.0 million dollars.

In both data sets, the mean is less than the median, which suggests that the distribution is skewed to the left. This means that there are some low values that are bringing down the mean.

However, we cannot conclusively say that the Security Company's employees were stealing based on this limited data. We would need to conduct a more thorough investigation and analysis to determine if there was any wrongdoing.