# What is the difference between average and weighted average?

In a world where data is king, it’s important to understand the ins and outs of all types of averages. When most people think of “average”, they’re thinking of what’s called the arithmetic mean. The arithmetic mean is simply calculated by adding up all of the numbers and dividing by how many numbers there are. However, using the arithmetic mean can produce misleading results in cases where some numbers are much more significant than others. This is where WA comes in!

Weighted averages take into account not just the quantity of data points but also their relative importance. For example, imagine you’re running a company with 100 employees. If 10 employees quit in one month, that would have a much bigger impact on your workforce than if 1 employee quits in 10 months. In this case, it would make more sense to weigh those 10 employees’ departures more heavily when calculating the average number of employees quitting each month. Weighted averages give a more accurate representation of reality by taking into account these fluctuations in data values.

When it comes to averages, weighted averages are almost always going to be better than simple arithmetic means. By understanding what they are and how they work, you can ensure that your business decisions are based on accurate information!

1. What is an average and what is a weighted average

2. How to calculate each type of average

3. When to use each type of average

4. The benefits of using a WA

5. The drawbacks of using a weighted average

## What is an average?

An average is the sum of all values divided by the number of values. There are different types of averages, but the most common type is the arithmetic mean. The arithmetic mean is what people generally think of when they hear the word “average”. To calculate the arithmetic mean, simply add up all of the numbers and divide by how many numbers there are. For example, let’s say you have the following data:

1, 2, 3, 4, 5

The arithmetic mean would be (1+2+3+4+5)/5= 3.

Weighted averages take into account not just the quantity of data points, but also their relative importance.

## What is a weighted average?

A WA is an average that gives more importance or “weight” to some values than others. The weight assigned to each value can be based on any criteria you choose, as long as it’s consistent. For example, you could weight data points by how recent they are, how accurate they are, or how important they are to your decision-making process.

To calculate a WA, you need two things:

1) a set of data, and

2) a set of weights.

The weights can be anything you want, as long as they add up to 1.0 (100%). For example, let’s say you have the following data:

1, 2, 3, 4, 5

And you want to weigh the data points as follows:

**Recent data: 0.4**

**Accurate data: 0.3**

**Important data: 0.3 **

The WA e would be (1*0.4)+(2*0.3)+(3*0.3)+(4*0.4)+(5*0.3)/5= 3.2. As you can see, the weighted average is slightly different from the arithmetic mean because it gives more importance to certain values than others.

### When should you use a WA?

WA are useful when you want to give more importance to certain values than others. For example, you might want to give more weight to recent data points because they’re more likely to be accurate than data points from the past. Or you might want to give more weight to important data points for your decision-making process.

There are many different ways you can weight data, so it’s important to think carefully about which weights make the most sense for your situation. If you’re not sure how to weigh your data, you can always consult with a statistician or other expert.

### What are the benefits of using a weighted average?

Weighted averages have several advantages over arithmetic means:

1. They’re more flexible: With weighted averages, you can give more or less importance to different values depending on your needs.

2. They’re more accurate: WA are often more accurate than arithmetic because they consider the relative importance of different values.

3. They’re easier to interpret: WA are often easier to interpret than arithmetic because they give you a better sense of the most important values.

#### What are the drawbacks of using a weighted average?

Weighted averages also have some disadvantages:

1. They can be difficult to calculate: Weighted averages can be tricky to calculate by hand, especially if you have a lot of data points.

2. They can be difficult to interpret: Weighted averages can be difficult to interpret if you’re not familiar with the concept.

3. They can be biased: If you’re not careful, weighted averages can be biased towards certain values.

#### How to calculate a weighted average in Excel

Calculating a weighted average in Excel is easy! Just follow these steps:

1. Enter your data into Excel.

2. In the cell next to each data point, enter the weight you want to use for that data point.

3. In the cell below your data, enter the following formula: =AVERAGE(B1:B5)*C1/SUM(C1:C5).

4. Press Enter to see the WA.

And that’s it! You’ve successfully calculated a WA in Excel.

Weighted averages are a powerful tool that can be used in many different situations. If you have data that you need to weigh, Excel is a great tool for doing so. Just remember to think carefully about which weights make the most sense for your data before you get started.

*I am studying at Middle East Technical University. I am interested in computer science, architecture, physics and philosophy.*

Love,

Cansu