Problem 20 - Basic Statistics for Business and Economics

Question

A report prepared for the governor of a western state indicated that 56 percent of the state's tax revenue went to education, 23 percent to the general fund, 10 percent to the counties, 9 percent to senior programs, and the remainder to other social programs. Develop a pie chart to show the breakdown of the budqet.

Step-by-Step Solution

Answer

Education: 56%, General Fund: 23%, Counties: 10%, Senior Programs: 9%, Other Social Programs: 2%.

Step 1: Determine the Percentage for Other Social Programs

First, we need to find the percentage of the budget allocated to 'Other Social Programs.' We know the percentages for education (56%), the general fund (23%), the counties (10%), and senior programs (9%). We need to subtract these percentages from 100% to find the remainder for the other social programs. So, calculate: \[100\% - (56\% + 23\% + 10\% + 9\%) = 100\% - 98\% = 2\%\]Thus, 2% of the budget is allocated to 'Other Social Programs.'

Step 2: Verify Total Percentage Adds Up to 100%

Add up all the provided percentages, including the calculated percentage for 'Other Social Programs,' to verify the total equals 100%.Calculate:\[56\% + 23\% + 10\% + 9\% + 2\% = 100\%\] The total is confirmed to be 100%, which means our calculations are correct.

Step 3: Create the Pie Chart

To create a pie chart, each sector (slice) of the chart will represent one part of the budget. Draw a circle to represent the entire budget. Then divide it into sections according to the percentages: - Education: 56% of the circle - General Fund: 23% of the circle - Counties: 10% of the circle - Senior Programs: 9% of the circle - Other Social Programs: 2% of the circle Each percentage corresponds to its respective portion of the circle.

Key Concepts

Budget Allocation

Budget allocation involves distributing available funds to different sectors within a given entity. In the case of the western state from the exercise, it's about how the state's tax revenue is divided. Each sector has its importance, leading to specific percentages assigned based on needs and priorities.

For this exercise:

• Education accounts for the largest portion with 56% of the allocation. This indicates a strong focus on educational priorities.
• The general fund receives 23%, often serving diverse state functions that are vital to the administration.
• Counties are allocated 10%, supporting local government services and infrastructure.
• Senior programs, at 9%, are essential for the wellbeing of elderly citizens.
• Other social programs receive the remaining 2%, covering miscellaneous needs that still require funding attention.

Understanding this breakdown helps in evaluating government priorities and planning financial strategies for effective resource use.

Percentage Distribution

Percentage distribution is a key tool for understanding how a whole is divided among its parts. It shows the proportion of each segment relative to the total. In our exercise, various percentages indicate how state revenue is allocated to different sectors.

Calculating accurate percentages involves adding known allocations and subtracting from the total (100%) to find missing values. This helps ensure the distribution is accurate. For instance, the undisclosed percentage for 'Other Social Programs' was discovered by subtracting the total known allocations from 100%.

This method not only checks accuracy but provides clarity on how comprehensive a budget is. It ensures each part receives rightful attention and helps highlight any sectors potentially underfunded or overfunded.

Visual Representation

Visual representation, such as a pie chart, makes data more accessible and easier to understand. A pie chart portrays data as 'slices' with size corresponding to the percentage value.

For instance, when representing budget allocations:

• Education's 56% allocation appears as the largest slice, making its priority clear instantly.
• Other segments like the general fund, counties, senior programs, and other social programs follow in descending order.

Creating a pie chart involves drawing a circle and partitioning it according to each category's percentage. This offers a visual, immediate grasp of complex numbers, allowing for quick comparisons and improved comprehension.

Such graphical reporting assists stakeholders in making informed decisions by visually highlighting areas of emphasis or need.

Step-by-Step Solution

The step-by-step solution for this exercise provides a clear roadmap to solving the problem. This approach not only verifies the calculations but also builds confidence in the solving process.

Every step involves careful planning:

• First, determining unknown values, like the 2% for 'Other Social Programs' using simple subtraction from the whole, helps organize and confirm data completeness.
• Second, verifying that all percentages add up to 100% ensures the allocation is watertight and error-free.
• Lastly, translating these values into a pie chart provides a tangible end-product that is visually blueprint.

Breaking down the problem into manageable steps aids problem-solving capabilities. It makes complex data less intimidating and helps students learn strategic ways to approach similar problems efficiently.