How to find average

Average a group of numbers

You may have used AutoSum to quickly add numbers in Excel. But did you know you can also use it to calculate other results, such as averages?

Use AutoSum to quickly find the average

AutoSum lets you find the average in a column or row of numbers where there are no blank cells.

Click a cell below the column or to the right of the row of the numbers for which you want to find the average.

On the HOME tab, click the arrow next to AutoSum > Average, and then press Enter.

Want more?

You may have used AutoSum to quickly add numbers in Excel.

But did you know you can also use it to calculate other results, such as averages?

Click the cell to the right of a row or below a column. Then, on the HOME tab, click the AutoSum down arrow, click Average, verify the formula if what you want, and press Enter.

When I double-click inside the cell, I see it is a formula with the AVERAGE function.

The formula is AVERAGE, A2, colon, A5, which averages the cells from A2 through A5.

When averaging a few cells, the AVERAGE function saves your time. With larger ranges of cells, it’s essential.

If I try to use the AutoSum, Average option here, it only uses cell C5, not the entire column.

Why? Because C4 is blank.

If C4 contained a number, C2 through C5 would be an adjacent range of cells that AutoSum would recognize.

To average values in cells and ranges of cells that aren’t adjacent, type an equals sign (a formula always starts with an equals sign), AVERAGE, open parenthesis, hold down the Ctrl key, click the desired cells and ranges of cells, and press Enter.

The formula uses the AVERAGE function to average the cells containing numbers and ignores the empty cells or those containing text.

For more information about the AVERAGE function, see the course summary at the end of the course.

Average

Averages are used to represent a large set of numbers with a single number. It is a representation of all the numbers available in the data set. The average is calculated by adding all the data values and dividing it by the number of the data point. The age of the students in a class is taken and an average is calculated to give a single value of the average age of the students of a class. Average has numerous applications in our day-to-day life. For quantities with changing values, the average is calculated and a unique value is used to represent the values.

Learning about average helps us to quickly summarize the available data. The large set of marks of the students, the changing price of the stocks, the weather data of a place, the income of different people in a city, are all examples for which we can calculate an average. Let us explore the page, to know more about the average.

What is the Meaning of Average?

The average is a numeric value which is a single representation of a large amount of data. The marks of the students of a class in a particular subject are averaged to give the average mark of the class. There is a need to know the performance of the entire class rather than the performance of each individual student. Here, the average is helpful. The average of a set of values is equal to the sum of the values divided by the individual values. Also, average is used in situations of changing values. The temperature of a place across the season is averaged to indicate the temperature of a place. The incomes of different employees in a company are averaged to know the income of the employees in a company.

It is sometimes difficult to make decisions based on one single data or a large set of data. Hence, the average value is taken and it helps to represent all the values in a single value

Definition of Average

The average is known as the arithmetic mean which is the sum of all numbers in a collection, divided by the count of the numbers present in the collection. In other words, the average is the ratio of the sum of all given observations to the total number of observations. Hence, the average formula is:

Average = Sum of the Observations/Number of Observations

Calculation of Average

The calculation of average follows three simple steps. Further, it includes the arithmetic operations: addition and division.

Step 1: Sum of the Numbers: The first step in the process of finding average is to find the sum of the given numbers. As an example, let us take the weight of six children. Find the sum of all the individual weights of the 6 children. 20lb, 25lb, 21lb, 30lb, 25lb, 26lb

Step 2: Number of Observations. Here we need to know the count or the data points. Here in our example of weights of children, we have 6 children. Count the total number of observations. Here, in this case, Zoe has a total of 6 observations which includes the weight of Zoe and her 5 friends. A total number of observations 6

Step 3: Average Calculation: Substituting the values from step 1 and step 2 in the average formula, we have the following expression. ​​

Average = Sum of the Observations/Number of Observations = 147/6 = 24.5lbs

Can Median Be Considered as Average?

No, the median is not considered as average. The average is the mean value of the data and is different from the median value of the data. Median is the middle value of a set of data arranged in increasing order. The median or middle value is also known as a central tendency. To find the measure of central tendency, we have to write the data points in increasing or decreasing order. Further, the calculation of the median depends on the number of data points. Let us look at the following two cases for the calculation of the median value.

For special cases of data having equally spaced data points, the average is equal to the median. Let us consider the numbers: 5, 10, 15, 20, and 25. The average of this data is equal to the sum(5 + 10 + 15 + 20 + 25) divided by 5. Hence the average of the data is 75/5 = 15. And the median is the middlemost value and it is equal to 15. The average and the median for this data is equal to 15.

Uses of Average

Average is useful in many ways in the real world. The average is useful to represent a single value for a large amount of data. A few examples of average are listed below.

☛Related Topics

Listed below are a few topics that are related to average.

Average Examples

Example 1: William has 3 boxes of cookies that have 3, 7, and 11 cookies each. What is the average cookie count per box?

Solution:

To find the average cookie count per box we need to divide the sum of the cookies by the total number of boxes. For the three boxes, the sum of the cookies is 3 + 7 + 11 = 21. The average cookies per box is the total number of cookies divided by the number of boxes. Hence the average = 21/3 = 7. Therefore the average cookie count per box is 7

Example 2: Rizo scored 70, 60, 80, and 50 marks in Math, English, Science, and Social Studies. What is the average mark he scored in the four subjects?

Solution:

To find the average we need to find the sum of the marks and divide it by the number of subjects. Here we have four subjects, Maths, Science, Social Studies, and English. Summing up all the scores we have 70 + 60 + 80 + 50 = 260. The average mark is equal to the sum of the scores divided by the number of subjects. Hence the average mark is 260/4 = 65. Therefore, the average marks scored in all the subjects is 65.

Example 3: The weight(lb) of students in a class are listed here: <60, 55, 54, 53, 51, 62>. Using the average formula, calculate the average weight of students in the class.

To find the average weight of students in a class.
Given:
Weights in lb: <60, 55, 54, 53, 51, 62>
Number of students = 6
Using Average Formula,
Average = (Sum of Observations) ÷ (Total number of Observations)
Average = <60 + 50 54 53 51 62>÷ <6>= 330/6 = 55. Therefore, the average weight of students in the class is 55.

SAT / ACT Prep Online Guides and Tips

How to Find the Mean of a Set of Numbers: Formula and Examples

Are you taking the SAT or ACT and want to make sure you know how to work with data sets? Or maybe you’re looking to refresh your memory for a high school or college math class. Whatever the case, it’s important you know how to find the mean of a data set.

We’ll explain what the mean is used for in math, how to calculate the mean, and what problems about the mean can look like.

What Is a Mean and What Is It Used For?

The mean, or arithmetic mean, is the average value of a set of numbers. More specifically, it’s the measure of a «central» or typical tendency in a given set of data.

Mean — often simply called the «average»— is a term used in statistics and data analysis. In addition, it’s not unusual to hear the words «mean» or «average» used with the terms «mode,» «median,» and «range,» which are other methods of calculating the patterns and common values in data sets.

Briefly, here are the definitions of these terms:

So what is the purpose of the mean exactly? If you have a data set with a wide range of numbers, knowing the mean can give you a general sense of how these numbers could essentially be put together into a single representative value.

For example, if you’re a high school student getting ready to take the SAT, you might be interested to know the current mean SAT score. Knowing the mean score gives you a rough idea of how most students taking the SAT tend to score on it.

How to Find the Mean: Overview

To find the arithmetic mean of a data set, all you need to do is add up all the numbers in the data set and then divide the sum by the total number of values.

Let’s look at an example. Say you’re given the following set of data:

$$6, 10, 3, 27, 19, 2, 5, 14$$

To find the mean, you’ll first need to add up all the values in the data set like this:

$$6 + 10 + 3 + 27 + 19 + 2 + 5 + 14$$

Note that you don’t need to rearrange the values here (though you may if you wish to) and can simply add them in the order in which they’ve been presented to you.

Next, write down the sum of all the values:

$$6 + 10 + 3 + 27 + 19 + 2 + 5 + 14 = \bo86$$

The last step is to take this sum (86) and divide it by the number of values in the data set. Because there are eight different values (6, 10, 3, 27, 19, 2, 5, 14), we’ll be dividing 86 by 8:

The mean, or average, for this set of data is 10.75.

How to Calculate a Mean: Practice Questions

Now that you know how to find the average —in other words, how to calculate the mean of a given set of data —i t’s time to test what you’ve learned. In this section, we’ll give you four math questions that involve finding or using the mean.

The first two questions are our own, whereas the second two are official SAT/ACT questions; as such, these two will require a little bit more thought.

Scroll past the questions for the answers and answer explanations.

Practice Question 1

Find the mean of the following set of numbers: 5, 26, 9, 14, 49, 31, 109, 5.

Practice Question 2

Practice Question 3

Source: 2018-19 Official ACT Practice Test

Practice Question 4

How to Find the Average: Answers + Explanations

Once you’ve tried out the four practice questions above, it’s time to compare your answers and see whether you understand not just how to find the mean of data but also how to use what you know about the mean to more effectively approach any math questions that deal with averages.

Here are the answers to the four practice questions above:

$$5 + 26 + 9 + 14 + 49 + 31 + 109 + 5 = \bo248$$

Next, take this sum and divide it by the number of values in the data set. Here, there are eight total values, so we’ll divide 248 by 8:

The mean and correct answer is 31.

Practice Question 2 Answer Explanation

Recall that to find the mean, you add up all the numbers in a set and then divide the sum by the total number of values.

$$4 + 4 + 2 + 11 + 6 + X + 1 + 3 + 2 = 36$$

The correct answer is 3.

Practice makes perfect!

Practice Question 3 Answer Explanation

This tricky-looking math problem comes from an official ACT practice test, so you can expect it to be a little less direct than your typical arithmetic mean problem.

Here, we’re given a data set with two unknown values:

We’re also given two critical pieces of information:

To solve for the mean of this data set, we will need to use all the information we’ve been given and will also need to know what the mode and median are.

As a reminder, the mode is the value that appears most frequently in a data set, while the median is the middle value in a data set (when all values have been arranged from lowest to highest).

We’re also told that the median is 25. To find the median, you must first rearrange the data set in order from lowest value to highest value.

We now have a complete data set with no unknown values:

15,15, 20, 30, 35, 41

All we have to do now is use these values to solve for the mean. Start by adding them all up:

Finally, divide the sum by the number of values in the data set (that’s six):

The correct answer is C. 26.

Practice Question 4 Answer Explanation

Have friends who also need help with test prep? Share this article!

Hannah received her MA in Japanese Studies from the University of Michigan and holds a bachelor’s degree from the University of Southern California. From 2013 to 2015, she taught English in Japan via the JET Program. She is passionate about education, writing, and travel.

Student and Parent Forum

Our new student and parent forum, at ExpertHub.PrepScholar.com, allow you to interact with your peers and the PrepScholar staff. See how other students and parents are navigating high school, college, and the college admissions process. Ask questions; get answers.

Ask a Question Below

Have any questions about this article or other topics? Ask below and we’ll reply!

JavaScript How to Calculate Average of an Array

Artturi Jalli

To calculate the average of an array in JavaScript:

This is the quick answer.

However, if this does not ring any bells, I recommend reading further.

In this guide, you learn how to calculate the average of an array of numbers in three different ways:

Before jumping into these, let’s make sure you understand what it means to calculate the average in the first place.

Average in Mathematics

In mathematics, the average is the middle value of a group of numbers. The average is also commonly called the mean or the arithmetic mean.

The average is calculated by dividing the sum of all the values by the number of values.

Example. Find the average age of a group of students in this table:

Solution. Let’s sum up the ages and divide the result by the number of students:

Calculating the average is a useful way to describe data in statistics.

For instance, you can calculate the average of your grades to get an idea of how well your studies are going.

Anyway, let’s jump into the coding part of this tutorial.

Let’s implement a basic JavaScript for loop to find the average first.

Find the Average with For Loop in JavaScript

Perhaps the most beginner-friendly way to find the average of a JavaScript array is by using a for loop for summing up the numbers.

Here is how to use a for loop to find the average of an array of numbers:

Although there is nothing wrong with this approach, we can make it way shorter and more concise.

Next up, you are going to learn how to use the forEach() function for calculating the average.

The following examples are more intermediate. Do not worry if you find them a bit tricky as a beginner!

Find the Average Using forEach()

In JavaScript, there is a built-in function called forEach().

This function is used to run a give function for each element in the array.

In other words, the forEach() function behaves a lot like a for loop. It iterates through the array and calls the given function for each element.

To find the average using forEach() function:

To make the forEach() add each number to the sum, it needs to take a function that accepts a number argument and adds it to the sum.

To make it a bit more concise, you can also use the arrow function notation in the forEach() function call:

Although this approach is a bit shorter than the for loop approach, it is still not the most elegant one.

Next, let’s use the reduce() function to find the average of an array of numbers.

This will make the process significantly more straightforward.

Find the Average Using reduce()

In JavaScript, there is a built-in function called reduce().

This function works the same way as folding in mathematics. Reducing means you fold a group of numbers into a single value.

For example, you can reduce or fold an array of numbers to get the sum of it.

The reduce() function takes a function as its argument. This is called a reducer.

It also takes an initial value for the accumulated result as its second argument.

Here is how the reduce() function and the reducer function operate on an array:

Now, let’s use the reduce() to find the average of a function.

Let’s take a moment to understand how this piece of code works:

As you can see, this piece of code is way shorter than the for-loop approach. Once you learn how to read the reduce() function a bit better, you notice how much simpler this piece of code is than the lengthy for loop.

To find a complete guide on how to use the reduce() function in JavaScript, feel free to read this article.

This completes the example.

Now you should have a great understanding of how to calculate the average of an array in JavaScript in a bunch of different-looking ways.

Before you go, let’s do a quick recap.

Conclusion

Today you learned how to calculate the average of an array in JavaScript.

To recap, the average is used in statistics to describe the centrality of a dataset.

To find the average (the mean), sum up the values and divide the sum by the number of values.

In JavaScript, there is a bunch of ways in which you can find the average. In this guide, you saw three common examples:

The latter approach is a bit tricky to wrap your head around as a beginner. However, it is a really short and concise way to get the job done.

Finding the average

Finding the average or the mean is a very straightforward concept. If you have a set of numbers, the average is found by adding all numbers in the set and dividing their sum by the total number of numbers added in the set.

We can generalize the concept of average with the formula below:

Let us illustrate with examples:

Get the average of the following set of numbers:

Sum = 5+4+12+2+1+6= 30

Divide 30 by 6 (the total number of numbers)

30 divided by 6 is 5, so the average or mean is 5

Get the average of the following set of numbers:

Sum = 5+10+20+5+10 = 50

Divide the 50 by 5 (the total number of numbers added)

50 divided by 5 is 10, so 10 is the average or mean.

Finding the average when the numbers in the set are the same.

When all the numbers in the set are the same, it is easy to find the average.

Find the average of the following set of numbers:

Find the average of the following set of numbers:

12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12

12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 = 132

What can we conclude from example #3 and example #4?

When the numbers in the set are all the same, the average is just the number itself.

Finding the average when some of the numbers in the set are negative numbers.

Mr. Peter collected 125 pencils from students during the past 5 days. On the average, how many pencils did he collect each day?

Average = 125/5 = 25

Last week, Samuel ordered pizza every day. After collecting all his receipts and getting the total, he realized that he spent a total of 63 dollars on pizza. On the average, how much money did he spend on pizza each day?