Problem 39 - Basic Statistics for Business and Economics

Question

Annual revenues, by type of tax, for the state of Georgia are as follows. Develop an appropriate chart or graph and write a brief report summarizing the information. $$ \begin{array}{|lr|} \hline \text { Type of Tax } & \text { Amount (000) } \\ \hline \text { Sales } & \$ 2,812,473 \\ \text { Income (Indlividual) } & 2,732,045 \\ \text { License } & 185,198 \\ \text { Corporate } & 525,015 \\ \text { Property } & 22,647 \\ \text { Death and Gift } & 37,326 \\ \text { Total } & \$ 6,314,704 \\ \hline \end{array} $$

Step-by-Step Solution

Answer

The majority of Georgia's tax revenue is from Sales and Individual Income taxes.

Step 1: Understand the Data

We have data on the annual revenue generated by different types of taxes in the state of Georgia. The tax categories and their respective amounts (in thousands) are listed in the table provided.

Step 2: Convert Data to Percentage

To better understand the distribution, calculate the percentage contribution of each tax type to the total revenue. Use the formula \( \text{Percentage} = \left( \frac{\text{Amount of a tax}}{\text{Total Revenue}} \right) \times 100 \).

Step 3: Compute Percentages

Let's calculate the percentage for each tax type:- Sales: \( \left( \frac{2,812,473}{6,314,704} \right) \times 100 \approx 44.54\% \)- Individual Income: \( \left( \frac{2,732,045}{6,314,704} \right) \times 100 \approx 43.26\% \)- License: \( \left( \frac{185,198}{6,314,704} \right) \times 100 \approx 2.93\% \)- Corporate: \( \left( \frac{525,015}{6,314,704} \right) \times 100 \approx 8.31\% \)- Property: \( \left( \frac{22,647}{6,314,704} \right) \times 100 \approx 0.36\% \)- Death and Gift: \( \left( \frac{37,326}{6,314,704} \right) \times 100 \approx 0.59\% \)

Step 4: Create a Chart

Using the percentages calculated, create a pie chart to visually represent the distribution of tax revenues. Each "slice" of the pie will represent a tax type's percentage of total revenue.

Step 5: Summarize the Information

Most of Georgia's tax revenue comes from Sales and Individual Income taxes, which together make up over 87% of the total. Smaller contributions come from Corporate taxes, with minor portions from License, Property, and Death and Gift taxes.

Key Concepts

Percentage Calculation

Understanding how to calculate percentages is crucial when analyzing data like tax revenue. It allows you to see each tax type's contribution to the total.

Let's break it down. Suppose you have a tax figure and a total revenue number. You can find the percentage contribution of this tax by using:

• The formula: \( \text{Percentage} = \left( \frac{\text{Amount of a tax}}{\text{Total Revenue}} \right) \times 100 \).
• This formula helps express how much a part contributes to the whole in percentage terms.
• Multiplying by 100 converts the decimal into a percentage, which is more intuitive to understand.

For instance, calculating the percentage for a tax amount of \(2,812,473 out of a total revenue of \)6,314,704, you'd find:

\[ \left( \frac{2,812,473}{6,314,704} \right) \times 100 \approx 44.54\% \]
This method can be applied to each tax type to determine its share of the overall revenue.
Effectively using percentage calculations can illuminate the relative importance of different revenue sources.

Data Visualization

Data doesn't just need to be calculated; it needs to be visualized too. This is where data visualization comes in.

Visualization helps convey complex data in an understandable way. Here, the goal is to represent the tax revenue data for Georgia.

Some key points to consider for effective data visualization include:

• Choosing the right chart type for your data.
• Ensuring the chart communicates the key message clearly.
• Using colors and design elements to enhance clarity.

The data visualization should turn numbers into a story. In this case, it shows how significant each tax type's contribution is to the total tax revenue.
Visual aids like charts and graphs help quickly compare, contrast, and identify patterns or outliers.
Using visualization tools effectively can make a world of difference in data interpretation.

Pie Chart

A pie chart is an excellent tool for visualizing data distribution. It's particularly useful when you're concerned with proportions and percentages, like in tax distribution.

Here's how a pie chart helps in this context:

• Each slice represents a category (in this case, a tax type).
• The size of the slice corresponds to the percentage of the total revenue that category represents.
• This provides an at-a-glance overview of large and small contributions.

Creating a pie chart involves plotting data on a circle, with each section proportional to the numbers it represents.
For Georgia's tax data, each tax type — from Sales to Death and Gift — is a slice, visually representing its percentage of the total.
This makes it easy to see, for example, how Sales and Individual Income taxes make up the majority of the revenue.
Pie charts allow for quick, intuitive insights into data breakdowns, making them a popular choice for financial data representation.

Tax Distribution

Tax distribution is the analysis and representation of how different types of taxes contribute to total revenue.

In Georgia's case, it's clear that some taxes contribute far more significantly than others:

• Sales and Individual Income taxes are responsible for the bulk of the collected revenue, highlighting their importance.
• Corporate Tax also plays its role but to a lesser extent.
• Smaller contributions come from License, Property, and Death and Gift taxes.

Understanding tax distribution helps policymakers, businesses, and citizens gauge the tax landscape.

This information may influence economic decisions and strategies, such as identifying areas that might need adjustment or reform.
Analyzing tax distribution is not just about knowing numbers; it's about understanding the financial backbone of a region.