Reading: Lesson 4 - Mathematics and Management

7.3.A - Mathematics and Management

1. MATHEMATICS SKILLS FOR MANAGERS

1.  Many factors influence decisions, but they do not all carry the same weight. Experience plays a role when managers consider similar situations and what worked or did not work in the past. Personal beliefs, values, and even intuition can influence a manager’s decisions. These factors can shape a manager’s approach to a decision and help identify some choices as better than others. However, they should not be the primary basis for making decisions because they do not take into consideration the specific information and conditions surrounding the decision to be made. Today, managers are skilled in data-based decision making.
   
2. Data-based decisions use information, facts, and measures, usually in numerical form, as the primary basis for choosing among alternatives. Managers gather and analyze information to keep decisions objective and as free from bias as possible. Because data are collected and analyzed in numerical form, managers rely on mathematics to help them understand and interpret the information in making effective decisions. Skill in the understanding and use of mathematics is important for all managers. Many of the applications involve basic arithmetic operations. You will also need to understand and use fractions, decimals, and basic units of measurement in both the U.S. and metric systems. Analysis of numerical data typically involves calculating percentages, ratios, and proportions.
   
3. The next level of mathematics skills needed in business involves understanding algebra. Algebra moves beyond completing arithmetic operations to the process of thinking logically using numbers, symbols, and equations to solve problems. Algebra requires the use of logic, understanding rules and procedures, and mastery of inductive and deductive reasoning. Inductive reasoning uses the analysis of specific data to draw broader conclusions while deductive reasoning takes general principles and uses them to make predictions about specific situations or circumstances.
   
4. Statistics are mathematical tools used for more advanced numerical analysis in business. Statistics involve the use of carefully selected numerical information to describe the situation being studied and to make predictions about future similar circumstances. For example, the manager of a manufacturing production line may want to know how many defective products to expect in the next six months. Rather than collecting information for the entire month and examining every product produced, the manager may sample three percent of the products produced during a two-hour period on five different days. That number is then used to estimate the total number of defective products to expect during the month. In the same way, a development team working on a new product wants to estimate the sales when a product is distributed nationwide. They cannot just guess how many units to manufacture to meet customer demand without having far more than they can sell. Therefore, they establish three test markets in cities that represent various parts of the country and sell the product for two months. Based on those sales and data from previously introduced new products, they are able to estimate nationwide sales and plan manufacturing based on the estimate.
   
5. Another important mathematical skill needed by managers is to be able to organize, analyze, and present data visually. When numerical information is initially collected, it is known as raw data. Raw data consist of information not yet processed for meaningful use. Raw data must be processed and organized to be understandable and useful for decision makers. Processed data (also known as information) are data that have been checked for accuracy and organized in a way to make them understandable and usable. Processed data can be classified, summarized, and compared in a more easily understood way than if presented as raw data. Well-developed spreadsheets, tables, charts, and graphs are excellent communication tools and make it easier to review and analyze large amounts of numerical information.
   

2. BUSINESS APPLICATIONS OF MATHEMATICS

1. Some uses of mathematics are common to all managers, while others are specific to the area of management or to unique business operations and activities. An important part of preparing to be a manager is understanding how mathematical operations are used in business and developing the necessary general and specific skills.
   
2. Using mathematics in business involves much more than being able to make the necessary calculations involved in a numerical problem. In fact, with easy access to calculators, including cell phone apps, there is often little need to be able to complete the full calculation mentally. In business, electronic database programs and spreadsheets have become the primary tools for analyzing data. Database programs categorize and store detailed information in the form of individual records that can be accessed and reorganized for varied uses. Electronic spreadsheets allow large amounts of data to be analyzed and updated using formulas along with charting and graphing tools. Managers should be comfortable using calculators, computers, and common business software. Even with access to easy-to-use electronic tools, managers need to develop mathematics skills for analyzing situations, determining the data needed to sup- port decision making, organizing the information in the correct way for analysis, and evaluating the results to make sure the solution is reasonable. Managers need mathematical skills to be able to calculate, compare, plan, analyze, and project. These skills are described in the Figure below. 
   

   
   

3. All parts of business operations use mathematics. Many common mathematics applications are used throughout a business, while some applications are unique to a specific business function or operation. In addition, each of the five management functions—planning, organizing, staffing, leading, and controlling— requires an understanding of math. A frequently used mathematical application in business is the budget. A budget is a financial tool used to project income and expenditures. Because money is a fundamental resource of businesses, managers must be able to accurately anticipate revenues and other sources of income for their part of the business. They also need to be able to identify and accurately predict all of the expenses. Other common tools used by managers that require mathematics are schedules, standards, business records, and research.
   
4. The functional area of business with the most extensive use of mathematics is accounting and finance. Accounting and finance managers manage the financial resources, maintain all financial records, prepare financial statements and reports, and communicate financial information and performance to owners, other managers, government agencies, and others who need the information.
   
5. Production and operations personnel are responsible for the ongoing operations of a business. They turn the resources of the organization into the products and services that are sold to customers. The major activities of production and operations that require math applications are forecasting, resource management (including the scheduling of personnel and production), purchasing, inventory management, and order fulfillment.
   
6. Marketers complete a variety of activities to identify markets, develop demand, and sell the products and services to maximize profitability. Almost all marketing activities include mathematics applications such as budget development, cost controls, pricing, advertising, sales planning, and managing financing and credit services. One of the most important areas of data collection and analysis is marketing research.
   
7. Human resources management includes the activities involved in acquiring, preparing, and compensating the people who do the company’s work. Major areas for human resource personnel that require mathematics skills are planning compensation and benefits programs and managing personnel records, including payroll, payroll taxes, and benefits. The human resources department is responsible for planning and documenting employee training and management development and maintaining data related to employee performance evaluations.