Difference Between Average and Mean – Definition With Examples

Welcome to another informative session on our Brighterly platform. As our mission is to bring light to the world of mathematics for children and make it more engaging, today, we are taking a detailed journey into the world of averages and means. For many, these terms may seem identical at first glance. However, the world of mathematics has a distinctive use and understanding for each term. By the end of this article, you’ll see these concepts with a new understanding and a more profound insight that will further illuminate your mathematical journey.

What are Average and Mean? – Definition With Examples

While both terms are widely used in mathematics and statistics, they’re often mistaken to be the same. They have different meanings, although they are closely related.

Definition of Average

The term “average” is a general term used in mathematics and statistics to represent a central or typical value in a set of data. In most everyday language, the term “average” is commonly used to refer to what is technically called the “arithmetic mean,” the sum of all numbers divided by the count of those numbers. For instance, if you have the numbers 2, 4, and 6, the average would be (2+4+6)/3 = 4.

Definition of Mean

On the other hand, the term “mean” is a statistical term that refers specifically to the arithmetic mean. It’s the sum of all the numbers in a dataset divided by the number of items in the dataset. For instance, if you have the numbers 5, 10, and 15, the mean would be (5+10+15)/3 = 10. Mean is just one type of average. There are others, such as the median and mode.

Properties of Average and Mean

Understanding the properties of these two terms can further clarify their definitions and their differences.

Properties of Average

One property of the average is that it’s greatly influenced by extreme values. For example, if you have the numbers 2, 4, 6, and 100, the average would be (2+4+6+100)/4 = 28, which is skewed towards the larger number. This property makes the average less reliable in datasets with outliers.

Properties of Mean

The mean shares the same property as the average, given that it’s also significantly influenced by extreme values. It’s a type of average, after all. However, the term “mean” specifies the type of average being used and makes it clear that it’s the arithmetic mean rather than any other kind.

Difference Between Average and Mean

The primary difference between the average and mean lies in their specificity. While the average can refer to the mean, median, or mode, the mean is specifically the sum of all numbers in a set divided by the count of those numbers.

Calculations of Average and Mean

Let’s take a look at how to calculate the average and mean.

Calculating an Average

To calculate the average of a set of numbers, you sum up all the numbers and then divide by the count of those numbers. It’s a simple and straightforward process.

Calculating a Mean

The process of calculating the mean is the same as calculating the average. You sum up all the numbers and then divide by the count of those numbers. The difference is in the terminology: when you say “mean,” you’re specifying that it’s the arithmetic mean.

Practice Problems on Average and Mean

Now that we’ve thoroughly covered the concepts of average and mean, it’s time to put that knowledge to the test with some practice problems. Remember, consistent practice is the key to mastery in mathematics. Let’s dive in!

Problem 1: Calculating an Average

Tom scored 85, 90, and 95 on his first three math exams. What is the average of his scores?

To find the average, add up all the numbers and then divide by the count of those numbers. So, we add 85 + 90 + 95 to get 270. Then, we divide 270 by 3 (the number of scores), which gives us an average score of 90.

Problem 2: Calculating a Mean

A group of friends recorded the number of pages they each read over the weekend: 100, 120, 80, 150, and 90. What is the mean number of pages read?

Similar to the first problem, we’ll add up all the numbers and then divide by the count. Adding 100 + 120 + 80 + 150 + 90 gives us 540. Dividing 540 by 5 (the number of friends) yields a mean of 108 pages.

Problem 3: Interpreting the Mean

If we have a dataset of 5, 7, 9, 12, and 20, what would happen to the mean if we added a 6th data point of 50?

First, let’s calculate the original mean: (5 + 7 + 9 + 12 + 20) / 5 = 10.6. Now, if we add a 6th data point of 50, the new mean becomes: (5 + 7 + 9 + 12 + 20 + 50) / 6 = 17.16. The mean is significantly affected by this outlier and increases, showing how sensitive the mean is to extreme values.

These problems offer a glimpse into the practical application of average and mean. For more comprehensive practice sets, you can explore the Brighterly. With practice, these concepts will become second nature, and you’ll be able to solve more complex problems with ease. Happy practicing!

Conclusion

Our exploration of the concepts of average and mean illuminates the remarkable beauty and precision of mathematics. These two concepts, though seemingly simple, hold the key to understanding complex data patterns and making informed decisions in real-world situations.

At Brighterly, we believe that every child has the potential to understand and appreciate the beauty of mathematics. We hope that this deeper understanding of average and mean will not only help you solve mathematical problems more effectively but also help you appreciate the role of mathematics in our world.

Remember, mathematics isn’t about memorizing formulas and rules; it’s about understanding concepts and applying them creatively. As you continue your learning journey with Brighterly, we hope you will carry this spirit of curiosity and exploration with you. Keep learning, stay curious, and let the world of mathematics brighten your way!

Here at Brighterly, we’re always ready to assist you in your learning journey. Feel free to reach out to us with any questions or concepts you’re struggling with, and let’s make learning mathematics a joyful experience.

Frequently Asked Questions on Average and Mean

What’s the difference between average and mean?

Although the terms “average” and “mean” are often used interchangeably in casual conversations, they hold different meanings in the realm of mathematics. “Average” is a broader term and can represent different types of central tendencies in a data set, such as the mean, median, or mode. On the other hand, “mean” is a specific type of average – the arithmetic mean. It is calculated by summing all the numbers in a set and dividing by the number of items in the set.

Are mean and average always the same?

Not always. In everyday language, they are commonly used interchangeably. However, in statistical language, mean is just one type of average. So while all means are averages, not all averages are means. It’s essential to know the context in which these terms are used.

Why is understanding average and mean important?

The understanding of average and mean is fundamental in statistics and mathematics. These concepts help us to summarize a data set into a single value that represents a “typical” value or central tendency of the data. This simplification can be crucial in understanding patterns in the data, making predictions, and making informed decisions in various fields such as business, science, economics, and more.

How are average and mean calculated?

Both average (when it refers to the arithmetic mean) and mean are calculated by summing all the numbers in a set and dividing by the count of those numbers. For example, to find the average or mean of 2, 4, and 6, you’d add the numbers to get 12, and then divide by 3 (because there are three numbers), giving you a mean or average of 4.

Information Sources
  1. Mean from Wikipedia.
  2. Understanding Averages from National Center for Education Statistics (NCES) Kids’ Zone.
  3. The Arithmetic Mean from Wolfram MathWorld.

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