# Application of Statistics in Business

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• 0:02 What Is Business Statistics?
• 0:34 Use of Descriptive Statistics
• 2:18 Use of Inferential Statistics
• 5:22 Lesson Summary
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Lesson Transcript
Instructor
Wendy A. Garland

Wendy has a Ph.D. in Adult Education and a Master's Degree in Business Management. She has 10 years experience working in higher education.

Expert Contributor
Jerry Allison

Jerry holds a Doctor of Business Administration and a Masterâ€™s in Mathematics. He has taught business, math, and accounting for over 25 years.

Statistics is used every day in business. This lesson describes some of the more popular applications to business statistics and provides real life examples of how it is used. Key vocabulary and terminology will also be discussed.

Business statistics is a specialty area of statistics which are applied in the business setting. It can be used for quality assurance, financial analysis, production and operations, and many other business areas. Just as in general statistics, there are two categories: descriptive and inferential. Descriptive statistics are used to describe the total group of numbers. Inferential statistics infers relationships from the population of numbers.

## Use of Descriptive Statistics

Descriptive statistics are used to summarize and describe total numbers. Looking at statistical numbers such as mean, or the average number, mode, or the most frequent number, or median, or the middle number, helps managers monitor business activities and make decisions. Often numbers themselves do not show the big picture, so ratios, or numbers representing relationships are used.

Perhaps you're a regional manager who oversees 15 different car dealerships. You will keep track of sales per month, number of vehicles sold, number of salesmen, sales per person, operational costs, delivery times, and other information. You use this statistical information to look at trends, understand relationships between numbers, and make sound business decisions. Perhaps you need to shift a sales member to a different store, or realize that you need more available stock during certain months, all of which helps maximize the company's resources and profit.

Or, perhaps, you're a regional store manager and are concerned about how long customers have to wait to check out. Currently, customers queue in multiple lines with a single cashier. You measure the mean length of time for customers to complete their transaction for a month. Then the next month, you line up customers in a single line with multiple cashiers and measure the mean length of time for the transaction. You notice that even though customers take longer to walk to the next available cashier, the overall transactions are reported faster. When the company expands and builds the next store, you specifically request it to be designed with one queuing line, using your findings to substantiate the request.

## Use of Inferential Statistics

Inferential statistics help managers draw conclusions based on limited data. When predicting the future, we don't have a magic crystal ball, but we do have statistical strategies, such as sampling, probability, and models.

Marketing departments often use inferential statistics. A company might issue a survey and ask questions about their products. However, it's impossible to survey every individual customer. The marketing department will determine the appropriate sample size, or the number of people to ask. Based on the results, statisticians can infer the responses are representative of the larger group of customers.

Finance departments use statistical modeling for predicting budgets and capital expenditures, when there are many unknown factors. A statistical model is a representation of what will probably happen. Unfortunately, economists can't predict everything so they use probability. Probability is simply the likelihood of something happening.

For example, let's say a company is taking out a loan for construction of a plant expecting it to be operational in 3 years. They are relying on the income from the plant to repay the loan. The finance team will run a statistical model that will include any possible delays, changes to building regulations, and catastrophic events. It's best to be prepared so it doesn't bankrupt the company if something goes wrong.

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## Statistics in Quality Assurance

### Manufacturing Scenario Discussion

We-B-Board manufacture tables at which people sit for classes. What measurements would you take on the tabletops to determine if the top was made satisfactorily?

#### Scenario Calculation 1

Suppose you visit those who make the tabletops for the tables mentioned above and these tops are supposed to be 5 feet long. If you take a sample of 4 tabletops and get lengths of 4.6 ft, 4.5 ft, 4.8 ft, 4.7 ft, and 4.6 ft, what is the mean, median, and mode of this sample? How far off is the average sample table from the standard? If this sample is representative of all of the tables manufactured, what is the probability that a table is less than 4.6 feet long?

#### Scenario Calculation 2

Bright Idea Manufacturing makes a bulb that is supposed to last for 5000 hours. The manufacturing process is designed to allow bulbs to be made that last between 4900 hours and 5100 hours, bulbs that don't last 4900 hours are rejected. What is the percentage change from 5000 hours that the process allows?

#### Scenario Calculation 3 and Research

Search the Internet and find three companies that have adopted the six-sigma philosophy. Also, find the percentage of defects that six sigma allows. If a company manufactures 5 million items, what is the maximum number of defects for a six sigma process?

#### Question 1

Is it possible the sample could be a bad sample and not show the true measurement? Why or why not? What could be done to try to make the data from the sample provide a better picture of the true population measurement?

#### Question 2

Suppose the average length from Scenario 1 is representative of the population average. What does that mean for the employees that glue precut laminate onto the tops? What does it mean for the workers attaching a precut frame to the table top?

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