Problem 22 - Basic Statistics for Business and Economics

Question

Shown below are the military and civilian personnel expenditures for the eight largest military locations in the United States. Develop a bar chart and summarize the results in a brief report. $$ \begin{array}{|lclc|} \hline \text { Location } & \begin{array}{c} \text { Amount Spent } \\ \text { (millions) } \end{array} & \text { Location } & \begin{array}{c} \text { Amount Spent } \\ \text { (millions) } \end{array} \\ \hline \text { St. Louis, M0 } & \$ 6,087 & \text { Norfolk, VA } & \$ 3,228 \\\ \text { San Diego, CA } & 4,747 & \text { Marietta, GA } & 2,828 \\ \text { Pico Rivera, CA } & 3,272 & \text { Fort Worth, TX } & 2,492 \\ \text { Arlington, VA } & 3,284 & \text { Washington, DC } & 2,347 \\ \hline \end{array} $$

Step-by-Step Solution

Answer

St. Louis, MO has the highest expenditure; Washington, D.C. the lowest.

Step 1: Understand the Data

We are given a list of eight military locations in the United States, along with their expenditures in millions of dollars. The goal is to represent these expenditures in a bar chart and summarize the information.

Step 2: Organize the Data

List out the locations with their corresponding expenditures: - St. Louis, MO: $6087 million - San Diego, CA: $4747 million - Pico Rivera, CA: $3272 million - Arlington, VA: $3284 million - Norfolk, VA: $3228 million - Marietta, GA: $2828 million - Fort Worth, TX: $2492 million - Washington, DC: $2347 million.

Step 3: Create a Bar Chart

Using a graphing tool or software, set the locations on the x-axis and the expenditures on the y-axis. Plot each location as a bar whose height corresponds to its expenditure amount. The bars should be clearly labeled with their respective values to allow for easy comparison.

Step 4: Analyze the Bar Chart

Observe the heights of the bars. St. Louis, MO has the highest expenditure, followed by San Diego, CA. The location with the lowest expenditure is Washington, D.C. This visualization makes it clear which locations have higher relative military and civilian personnel expenditures.

Step 5: Summarize Results

St. Louis, MO spent the most on military and civilian personnel. The expenditures span a range from $6087 million to $2347 million across the analyzed locations. The bar chart provides a clear visual representation of how these funds are distributed among different areas.

Key Concepts

Bar Chart

A bar chart is a popular type of data visualization commonly used in statistics. It displays information using rectangular bars. The length of each bar corresponds to the value it represents, making it easy to compare different categories at a glance. In the context of our exercise, a bar chart is a perfect tool to visualize expenditures across different military locations.

To create a bar chart:

• Start by selecting a tool or software that supports chart creation (like Excel or Google Sheets).
• Organize your categories—in this case, the locations—along the x-axis.
• The y-axis should represent the numeric values, such as the amount of money spent.
• For each location, draw a bar that reaches up to the value corresponding to the expenditure amount.
• Ensure bars are labeled clearly with both the location names and the expenditure amounts for clarity.

This method allows for a straightforward visual analysis, helping to identify which areas have the highest or lowest expenses.

Data Analysis

Data analysis is the process of inspecting, cleaning, transforming, and modeling data with the goal of discovering useful information. It's a crucial step in the statistical process as it allows us to draw meaningful conclusions from raw data. In our exercise involving military expenditures, data analysis helps us understand the distribution of funds across different locations.

Key steps in data analysis include:

• Understanding your dataset: Identify what the numbers represent and what each category means.
• Organizing data: Arrange your data in a logical manner, such as by location or expenditure, to facilitate analysis.
• Visualizing data: Create visual aids (like the bar chart) to see patterns and trends.
• Interpretation: Examine the visualized data to draw insights, such as which location spends the most or least.

The ultimate aim is to glean insights that can lead to informed decision-making, strategic planning, or policy development.

Statistical Representation

Statistical representation is the art of presenting data in a way that makes patterns, differences, and trends evident. This can involve both numerical summaries and graphical displays. In our example, statistical representation is achieved through the use of a bar chart, which provides a clear and immediate picture of spending habits across various military locations.

Elements of statistical representation:

• Clear labeling: Each data point or category should be easily identifiable.
• Accurate graphics: Graphs or charts (like the bar chart) should accurately reflect the data they're representing.
• Comprehensive summaries: Accompany visual data with textual summaries to provide a complete picture.

By focusing on clear, concise, and accurate representations, we ensure that the data is accessible and understandable to everyone, regardless of their statistical background. This leads to better interpretation and application of data findings.