Back To Course

Business 110: Business Math10 chapters | 78 lessons | 10 flashcard sets

Watch short & fun videos
**
Start Your Free Trial Today
**

Start Your Free Trial To Continue Watching

As a member, you'll also get unlimited access to over 70,000 lessons in math, English, science, history, and more. Plus, get practice tests, quizzes, and personalized coaching to help you succeed.

Free 5-day trial
Your next lesson will play in
10 seconds

Lesson Transcript

Instructor:
*Yuanxin (Amy) Yang Alcocer*

Amy has a master's degree in secondary education and has taught math at a public charter high school.

After watching this video lesson, you will be able to calculate any kind of average, even the average of certain events when some events repeat. Learn the general formula to use to calculate any average.

Everyone has a statistic. It is from these statistics that we get **averages**, or typical values. We can say that the average pay of an office worker is $12 per hour. Even though the average pay of an office worker is $12 per hour, you may not get paid exactly that much if you found an office job. Because the average is found by calculating the typical value of a large group of numbers, your pay could be more or less than $12. The way averages work is that if you found an office job that pays you $13 an hour, then you know that someone else has an office job that pays less than $12, $11 an hour for example. Why? Because after making the calculations, you have to get an answer of $12. If everyone got a pay higher than $12, then the average must be also be higher than $12. If we asked just a few office workers what their pay is, and we got answers of $10, $11, $12, $13, and $14, we would find an average of $12.

We will talk about the formula in just a bit. These numbers are spread out evenly. However, most often, our numbers are not spread out this evenly. You will find that some numbers repeat more often than others.

When some of your numbers repeat more often than others, we call their average a **weighted average** because the numbers that repeat more often than others will bring the average closer to those numbers. In the real world, we find weighted averages more common than averages where the numbers are spread out evenly. For example, in the real world, when you ask office workers about their pay, you might find that you get these answers: $9, $11, $12, $12, $12, $13, and $15. Do you see how the $12 is repeated? Even though we have these two kinds of averages, the formula we use to find our averages is the same.

What is this formula? It is this:

The *w* stands for the weight, or how many times *x* happens, and *x* stands for our data. The symbol before these letters is the summation symbol that tells you to add everything up. What this formula is telling you to do is to multiply each different data by the number of times it appears, sum it all up, then divide by the total number of data points that you have.

Let's use this formula to calculate the averages of the pay of office workers. The first set of data we have is $10, $11, $12, $13, and $14. We have five different data numbers, five different *x*'s: $10, $11, $12, $13, and $14. Each of these numbers happens just once, so *w* is 1 for each of these. Summing it all up we have (1 * $10) + (1 * $11) + (1 * $12) + (1 * $13) + (1 * $14) = 60. We then divide it by the total of our *w*'s. We have 1 + 1 + 1 + 1 + 1 = 5. So, 60 / 5 = 12. Our average pay is $12, which is what we expect. This is the average where our data is spread out evenly.

Let's look at finding the weighted average now. Our data is now $9, $11, $12, $12, $12, $13, and $15. We see that our $12 repeats. So, how many different data values do we have? We have 5. We can create a table to help us out with our calculations. In the first column, we will write our *w* values, the number of times each value repeats. In the second column, we will write our *x* values. Our $9 repeats once, our $11 repeats once, our $12 repeats three times, our $13 repeats once, and our $15 repeats once. Our table looks like this all filled in now:

w | x |
---|---|

1 | $9 |

1 | $11 |

3 | $12 |

1 | $13 |

1 | $15 |

Now, we can go ahead with our calculations based on our formula. We multiply our *w* with our *x* and then add them all up. We get (1 * $9) + (1 * $11) + (3 * $12) + (1 * $13) + (1 * $15) = 84. Now, we need to add up all our *w*'s. We get 1 + 1 + 3 + 1 + 1 = 7. Dividing 84 by 7, we get $12. Our average pay is $12 as expected.

What is basically happening in both of these examples is that we are adding up all our data points and then dividing by the total number of data points. This is a good way to check your work as well. The number you are dividing by must equal the total number of data points you collected. The top number must equal the sum of each individual data point.

Let's review what we learned now. An **average** is a typical value, and a **weighted average** is the average of a set of numbers where some of the numbers repeat. The formula to find any kind of average is this.

The *x* stands for a data value, and the *w* stands for the weight, or number of times each *x* repeats itself. The formula is telling us to multiply each different data value with its weight, or the number of times it repeats itself, and then we divide it by the sum of the weights, or the total number of data points.

After finishing this lesson, you should be able to:

- Recognize the difference between an average and a weighted average
- Demonstrate how to find an average using the proper formula

To unlock this lesson you must be a Study.com Member.

Create
your account

Already a member? Log In

BackDid you know… We have over 95 college courses that prepare you to earn credit by exam that is accepted by over 2,000 colleges and universities. You can test out of the first two years of college and save thousands off your degree. Anyone can earn credit-by-exam regardless of age or education level.

To learn more, visit our Earning Credit Page

Not sure what college you want to attend yet? Study.com has thousands of articles about every imaginable degree, area of study and career path that can help you find the school that's right for you.

You are viewing lesson
Lesson
8 in chapter 5 of the course:

Back To Course

Business 110: Business Math10 chapters | 78 lessons | 10 flashcard sets

- How to Calculate Mean, Median, Mode & Range 8:30
- Calculating the Standard Deviation 13:05
- Probability of Simple, Compound and Complementary Events 6:55
- Probability of Independent and Dependent Events 12:06
- Statistical Significance: Definition & Calculation 7:14
- Expected Value in Probability: Definition & Formula 7:14
- Normal Distribution & Shifts in the Mean 6:00
- Identifying & Calculating Averages 5:37
- Go to Probability and Statistics for Business

- Developing Adaptable Teams & Employees
- Effective Delegation Skills for Supervisors
- ORELA Essential Academic Skills: Practice & Study Guide
- Math 108: Discrete Mathematics
- ORELA Elementary Education - Subtest II: Practice & Study Guide
- Developing Adaptable Employees
- Proactive Employees & Team Problem Solving
- Organizational Change Management
- Identifying Competencies & Training Needs
- Relations Between Labor & Management
- How to Request a CLEP Transcript
- CLEP Exam Dates & Testing Center Locations
- CLEP Scoring System: Passing Scores & Raw vs. Scaled Score
- Continuing Education Opportunities for Molecular Biology Technologists
- WV College & Career Readiness Standards for Social Studies
- Common Core State Standards in Ohio
- Resources for Assessing Export Risks

- Required Rate of Return (RRR): Formula & Calculation
- Fixed Phrases: Definition, Examples & Practice
- Why Do Workers Join Unions? - Benefits & Reasons
- Rigid Motion in Geometry
- Electronic Health Records & Evidence-Based Medicine
- Symmetry in Insects: Types & Examples
- Native American Mathematics: History & Mathematicians
- Behavioral Health Quality: Framework & Measurement
- Quiz & Worksheet - Animal Population Size
- Quiz & Worksheet - Psychoanalyst Anna Freud
- Quiz & Worksheet - Potassium Chromate
- Quiz & Worksheet - Understsanding Transaction Processing Systems
- Quiz & Worksheet - Decomposing Numbers
- Tourism Marketing Flashcards
- Tourism Economics Flashcards

- Physical Science: High School
- Introduction to Public Speaking: Certificate Program
- GACE Behavioral Science: Practice & Study Guide
- Managing a Virtual Team
- Business Law Syllabus Resource & Lesson Plans
- AP Chemistry: Nuclear Chemistry
- Research Methods and Ethics
- Quiz & Worksheet - The Bosnian Genocide
- Quiz & Worksheet - The Al-Anfal Campaign
- Quiz & Worksheet - Ancient Greek Literature's Influence on Modern Literature & Language
- Quiz & Worksheet - Mala in se
- Quiz & Worksheet - Road Rage: Causes & Effects

- The Spread of Buddhism in Tang China
- Treasury Yield Curve: Definition & Historical Data
- Yellow Journalism Lesson Plan
- CSET Math Requirements
- Bill of Rights Lesson Plan
- Persuasive Writing Lesson Plan
- Magna Carta Lesson Plan
- The Lorax Lesson Plan
- Study.com Demo for Enterprise
- CSET Math Test Dates
- The Masque of the Red Death Lesson Plan
- Writing Prompts for Kids

Browse by subject