91Ó°ÊÓ

Find the mean and median for each of the two samples, then compare the two sets of results. Listed below are amounts (in millions of dollars) collected from parking meters by Brinks and others in New York City during similar time periods. A larger data set was used to convict five Brinks employees of grand larceny. The data were provided by the attorney for New York City, and they are listed on the Data and Story Library (DASL) website. Do the limited data listed here show evidence of stealing by Brinks employees? \(\begin{aligned} &\begin{array}{l} \text { Collection Contractor } \\ \text { Was Brinks } \end{array} & 1.3 & 1.5 & 1.3 & 1.5 & 1.4 & 1.7 & 1.8 & 1.7 & 1.7 & 1.6 \\ &\begin{array}{l} \text { Collection Contractor } \\ \text { Was Not Brinks } \end{array} & 2.2 & 1.9 & 1.5 & 1.6 & 1.5 & 1.7 & 1.9 & 1.6 & 1.6 & 1.8 \end{aligned}\)

Step by step solution

01

- List Data

Identify and list the two data sets given. For Brinks: 1.3, 1.5, 1.3, 1.5, 1.4, 1.7, 1.8, 1.7, 1.7, 1.6. For Non-Brinks: 2.2, 1.9, 1.5, 1.6, 1.5, 1.7, 1.9, 1.6, 1.6, 1.8.

02

- Calculate Mean for Brinks

Sum all Brinks amounts: 1.3 + 1.5 + 1.3 + 1.5 + 1.4 + 1.7 + 1.8 + 1.7 + 1.7 + 1.6 = 15.5. Divide by number of observations (10): \(\text{Mean} = \frac{15.5}{10} = 1.55\).

03

- Calculate Mean for Non-Brinks

Sum all Non-Brinks amounts: 2.2 + 1.9 + 1.5 + 1.6 + 1.5 + 1.7 + 1.9 + 1.6 + 1.6 + 1.8 = 17.3. Divide by number of observations (10): \(\text{Mean} = \frac{17.3}{10} = 1.73\).

04

- Sort Data for Median Calculation

Sort each list. Brinks: 1.3, 1.3, 1.4, 1.5, 1.5, 1.6, 1.7, 1.7, 1.7, 1.8. Non-Brinks: 1.5, 1.5, 1.6, 1.6, 1.6, 1.7, 1.8, 1.9, 1.9, 2.2.

05

- Calculate Median for Brinks

For an even number of observations, the median is the average of the two middle numbers. The middle numbers for Brinks are 1.5 and 1.6. \(\text{Median} = \frac{1.5 + 1.6}{2} = 1.55\).

06

- Calculate Median for Non-Brinks

For an even number of observations, the median is the average of the two middle numbers. The middle numbers for Non-Brinks are 1.6 and 1.7. \(\text{Median} = \frac{1.6 + 1.7}{2} = 1.65\).

07

- Comparison

Compare the means and medians: Brinks mean (1.55) and median (1.55) are less than Non-Brinks mean (1.73) and median (1.65).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

headline of the respective core concept

When we perform data analysis, we are collecting, organizing, and studying patterns in data sets. This exercise involves finding the mean and median for amounts collected from parking meters.
Let’s break down the steps involved.

• First, we listed the data for collections by Brinks and Non-Brinks contractors.
• Next, we calculated the mean for each group by summing all the amounts and dividing by the number of observations.
• After calculating the mean, we found the median. Sorting each dataset and finding the middle values allows us to pick the central tendency.

The purpose is to analyze data to conclude if there’s any significant difference between amounts collected by Brinks and other contractors, potentially indicating misappropriation. Understanding these calculations helps in various fields such as economics, crime analysis, and policy-making.

headline of the respective core concept

With statistical comparison, we can identify differences and similarities within data sets. By examining the means and medians, we compare two groups (Brinks vs. Non-Brinks).
The steps include:

• Calculating the mean: Brinks mean is 1.55 and Non-Brinks mean is 1.73. The difference suggests that Non-Brinks contractors collected more.
• Calculating the median: For Brinks, the median is 1.55, while Non-Brinks is 1.65. Similar to means, the medians also indicate Non-Brinks collected higher amounts.
• Result interpretation: These comparisons provide statistical evidence that can be used to detect inconsistencies or potential issues like theft.

In this exercise, the focus was on determining whether Brinks employees were involved in larceny by comparing collections. Such analyses are fundamental in research and diagnostics.

headline of the respective core concept

Crime statistics illustrate crime incidents through quantitative data, helping in understanding crime trends and patterns.
In this case, calculating means and medians can show if collections by Brinks employees were anomalous.
Let’s analyze further:

• The calculations here highlighted that Brinks had lesser mean and median collections, implying a difference worth investigating further for potential theft.
• Such analyses form a foundation for law enforcement and policy implementations.
• It allows agencies to take preemptive steps to ensure transparency and mitigate issues of theft and fraud.

By assessing and comparing data, officials can pinpoint discrepancies that warrant closer scrutiny. This proactive data-driven approach helps maintain the integrity of operations and uphold justice.