Problem 16 - Basic Statistics for Business and Economics with Student

Question

Andrews and Associates specialize in corporate law. They charge \(\$ 100\) an hour for researching a case, \(\$ 75\) an hour for consultations, and \(\$ 200\) an hour for writing a brief. Last week one of the associates spent 10 hours consulting with her client, 10 hours researching the case, and 20 hours writing the brief. What was the weighted mean hourly charge for her legal services?

Step-by-Step Solution

Answer

The weighted mean hourly rate is \(\$143.75\) per hour.

Step 1: Identify the Hourly Charges

First, identify the hourly charge for each type of service provided. \( \text{Researching: } \\(100 \text{ per hour} \), \( \text{Consultations: } \\)75 \text{ per hour} \), \( \text{Writing briefs: } \$200 \text{ per hour} \).

Step 2: Determine the Time Spent on Each Activity

Calculate the total number of hours spent on each type of activity. According to the problem, the associate spent \(10\) hours on consultations, \(10\) hours researching, and \(20\) hours writing the brief.

Step 3: Calculate the Total Charge for Each Service

Multiply the number of hours by the hourly rate for each activity: - Researching: \(10 \text{ hours} \times \\(100 = \\)1000\) - Consultations: \(10 \text{ hours} \times \\(75 = \\)750\) - Writing briefs: \(20 \text{ hours} \times \\(200 = \\)4000\).

Step 4: Compute the Total Revenue

Add the charges from all services to find the total revenue. \( \text{Total revenue} = \\(1000 + \\)750 + \\(4000 = \\)5750\).

Step 5: Calculate the Weighted Mean Hourly Rate

Use the formula for the weighted mean: \[ \text{Weighted Mean} = \frac{\text{Total Revenue}}{\text{Total Hours Worked}} \]The total hours worked is \(10 + 10 + 20 = 40\) hours. Thus, \[ \text{Weighted Mean} = \frac{\\(5750}{40} = \\)143.75 \text{ per hour.} \]

Key Concepts

Hourly Charge Calculation

The concept of hourly charge calculation is particularly useful for businesses offering services, such as law or consulting. It enables the determination of how much to charge clients based on the time spent on various activities. In our example, Andrews and Associates provides three different types of services, each with its own hourly rate:

• Research: $100 per hour
• Consultation: $75 per hour
• Brief Writing: $200 per hour

To calculate the total cost for each service, multiply the hours worked by the respective hourly rate. For instance, spending 10 hours on consultation at $75 per hour results in a charge of $750. Understanding these charges is crucial for preparing invoices and estimating project costs. By knowing how to calculate these charges, businesses can ensure they cover their expenses and achieve a desired profit margin. It also offers transparency to clients about how their fees are structured.

Corporate Law Services

Corporate law services involve various intricate legal procedures and documentation which require specialized knowledge. The services provided by law firms such as Andrews and Associates can include:

• Researching legal precedents and regulations
• Consulting with clients about their legal rights and obligations
• Drafting and writing legal briefs and documents

These services support businesses in navigating legal challenges and ensuring compliance with laws. The hourly charge for each service reflects the intensity and expertise required. For example, writing a brief is charged at a higher rate due to its complexity and the level of detail involved. This high level of service helps businesses confidently handle complex situations, boosting their operational success.

Statistics in Business

Statistics play a crucial role in the business world by helping to analyze data and make informed decisions. One application is calculating the weighted mean, particularly in service-based industries. The weighted mean provides an average rate that accounts for the time spent on each task. In the example of Andrews and Associates, the weighted mean helps the firm understand the average amount earned per hour across different services.The formula for the weighted mean is: \[\text{Weighted Mean} = \frac{\text{Total Revenue}}{\text{Total Hours Worked}}\]This calculation involves summing the entire earned revenue and dividing it by the total hours worked. For the associate who worked 40 hours in total, the weighted mean of $143.75 per hour gives a clear view of the overall productivity.Using statistics like the weighted mean aids businesses in evaluating performance, predicting future trends, and setting strategic goals. By understanding these statistics, businesses can optimize their service offerings and improve profitability.