How to Find the Average: A Simple Guide with Examples (2026)

Learning how to find the average is one of the most useful math skills you will ever pick up. You use it to work out a test score, a weekly temperature, a monthly bill, or a team’s points per game. The good news is that the method is short: add the numbers, count them, and divide. This guide shows you exactly how to find the average, step by step, with worked examples you can follow, the formula explained in plain words, and the mistakes that trip most people up. By the end, you will be able to find the average of any list of numbers — and you will know when the average is not the right number to use.

How to Find the Average in 3 Steps

Here is the whole method. It works for test scores, prices, temperatures, times, and any other list of numbers.

Step 1: Add all the numbers together. This gives you the sum.

Step 2: Count how many numbers you added. This gives you the count.

Step 3: Divide the sum by the count. The answer is the average.

That is it. If you remember only one thing from this article, remember this: average = sum / count.

A quick check before you trust your answer: the average must always lie between the smallest and the largest number in your list. If your answer is bigger than the biggest number, or smaller than the smallest number, you made a mistake in step 1 or step 2. Go back and add again.

What Is an Average?

An average is a single number that represents a whole set of numbers. Instead of listing ten test scores, you can say “the average score was 78” and everyone gets the picture at once. In everyday use, “average” usually means the arithmetic mean — add everything up and divide by how many things there are. In statistics, “average” is a wider idea. It covers three measures of central tendency: the mean, the median, and the mode. Each one describes what is typical in a different way, and this guide explains all three so you can pick the right one.

The average is useful because it turns a long list into one number you can compare. A class average of 78 and a class average of 84 tell you at a glance which class did better, without reading forty separate scores. Averages show up everywhere: in school grades, in sports, in weather reports, in business, and in everyday decisions like comparing prices.

The Average Formula

The average formula is simple:

Average = Sum of all values / Number of values

Written with symbols, if your values are x1, x2, x3, and so on up to xn, the mean is:

Average = (x1 + x2 + x3 + … + xn) / n

Here, n is how many values you have. The symbol for the sample mean is x with a bar over it (x̄), and the symbol for the population mean is the Greek letter mu (μ). You do not need to remember the symbols to use the formula — they are just shorthand for “add everything up and divide by how many there are.”

Symbol	Meaning
x̄ (x-bar)	The average (mean) of the data set
x1, x2, …, xn	The individual values in the data set
n	The total count of values
Σ (sigma)	Summation — “add everything up”

Worked Examples

The best way to learn how to find the average is to work through examples. Each one below shows every step, so you can follow along with a pencil or a calculator.

Example 1: Average Test Score

A student scores 68, 74, 81, 90, and 77 on five tests. What is the average score?

Step 1: Add the values. 68 + 74 + 81 + 90 + 77 = 390.
Step 2: Count the values. There are 5 tests, so n = 5.
Step 3: Divide. 390 / 5 = 78.

The average test score is 78. Check: 78 lies between the lowest score (68) and the highest (90), so the answer is sensible.

Example 2: Average Temperature

A town records these midday temperatures over five days: 24.5, 26.0, 23.5, 25.5, and 27.0 degrees. What was the average temperature?

Step 1: Add the values. 24.5 + 26.0 + 23.5 + 25.5 + 27.0 = 126.5.
Step 2: Count the values. n = 5.
Step 3: Divide. 126.5 / 5 = 25.3.

The average temperature was 25.3 degrees. Notice that the answer keeps the unit — an average of temperatures is itself a temperature, not a plain number.

Example 3: Average Price

Four items cost $12.99, $9.50, $15.00, and $11.25. What is the average price?

Step 1: Add the values. 12.99 + 9.50 + 15.00 + 11.25 = 48.74.
Step 2: Count the values. n = 4.
Step 3: Divide. 48.74 / 4 = 12.185, which rounds to $12.19.

The average price is about $12.19. Averages are often decimals, even when the question looks simple — that is normal, and rounding to two decimal places is fine for money.

Example 4: Average with Negative Numbers

Find the average of 5, -3, and 10.

Negative numbers are treated just like positive ones. They are included in the sum and in the count.

Step 1: Add the values. 5 + (-3) + 10 = 12.
Step 2: Count the values. n = 3.
Step 3: Divide. 12 / 3 = 4.

The average is 4. A common mistake here is to leave the negative number out, or to add its absolute value instead. Keep the minus sign in the sum and the method works exactly the same.

Example 5: Average of Two Numbers and Three Numbers

The average of two numbers is just their sum divided by 2. For 10 and 20, the average is (10 + 20) / 2 = 15. The average of three numbers is their sum divided by 3. For 10, 20, and 30, the average is (10 + 20 + 30) / 3 = 60 / 3 = 20. These tiny examples are worth doing by hand once, because they make the method feel obvious — and then the same method scales up to fifty numbers without changing.

Mean vs Median vs Mode

Mean, median, and mode are the three main types of average. They often give different answers for the same data, and knowing which one to use is half the skill.

Mean: the sum divided by the count. This is the average most people mean, and it uses every value in the set.
Median: the middle value when the numbers are arranged from smallest to largest. If there is an even number of values, the median is the average of the two middle values.
Mode: the value that appears most often. A set can have one mode, more than one mode, or no mode at all if every value appears once.

Measure	What it does	When to use it
Mean (arithmetic average)	Sum / count	Data is fairly even, with no extreme values
Median	Middle value when sorted	Data is skewed or has outliers, like income or house prices
Mode	Most frequent value	Categorical data, or finding the typical choice
Midrange	(Minimum + maximum) / 2	A quick estimate using only the two extremes

A short example shows the difference. Take the numbers 20, 22, 24, 26, and 200. The mean is (20 + 22 + 24 + 26 + 200) / 5 = 292 / 5 = 58.4. The median is 24, the middle value when sorted. The mode does not exist here, because every value appears once. The mean (58.4) is much higher than most of the data, while the median (24) describes the typical value far better. That is why the next section matters.

There are two more averages worth knowing by name. The geometric mean is the nth root of the product of n positive numbers, and it is used for growth rates and ratios, where multiplying matters more than adding. The midrange is the average of the minimum and the maximum. Neither replaces the mean for everyday problems, but you will meet them in statistics and finance.

How to Find a Missing Number from the Average

This is a classic homework problem, and it is easier than it looks. The trick is to work the formula backwards.

Suppose the average of five numbers is 18, and four of the numbers are 12, 16, 20, and 24. What is the fifth number?

Step 1: Multiply the average by the count to get the total sum. 18 x 5 = 90. So all five numbers must add up to 90.
Step 2: Add the numbers you already know. 12 + 16 + 20 + 24 = 72.
Step 3: Subtract. 90 – 72 = 18.

The missing number is 18. Check it: (12 + 16 + 20 + 24 + 18) / 5 = 90 / 5 = 18, which matches the given average.

The general rule is: missing number = (average x count) – sum of the known numbers. Whenever a question gives you an average and all but one value, this is the method to use.

Weighted Averages

Sometimes not every number should count the same. A final exam may be worth more than a homework assignment, or a large class may matter more than a small one. That is when you need a weighted average.

The weighted average formula is:

Weighted average = (value x weight added up) / total weight

Worked example: an exam score of 90 has a weight of 3, and homework of 80 has a weight of 2.

Step 1: Multiply each value by its weight. 90 x 3 = 270, and 80 x 2 = 160.
Step 2: Add the products. 270 + 160 = 430.
Step 3: Add the weights. 3 + 2 = 5.
Step 4: Divide. 430 / 5 = 86.

The weighted average is 86. Notice that the plain average of 90 and 80 would be 85 — close, but wrong, because it ignores the weights. Whenever the items being averaged are not equally important, use the weighted formula. Grade averages are the most common example: a course grade is usually a weighted average of exams, homework, and projects, not a plain average of the scores.

Averages of Percentages, Times, and Grouped Data

Averages of percentages. You can average percentages directly when they are equally weighted and refer to comparable things. For 70%, 80%, and 90%, the average is (70 + 80 + 90) / 3 = 80%. But if the percentages come from groups of different sizes, do not average them directly. Combine the underlying totals instead, or use a weighted average. Averaging the pass rates of a class of 10 and a class of 100 as if they were equal would give the small class far too much influence.

Averages of times. Convert each duration to the same unit first, then average, then convert back. For durations of 1 minute 30 seconds, 2 minutes, and 2 minutes 30 seconds, convert to seconds: 90, 120, and 150. The average is (90 + 120 + 150) / 3 = 120 seconds, which is 2 minutes. Clock times that cross midnight need extra care, because 11:00 p.m. and 1:00 a.m. are two hours apart, not ten.

Grouped and frequency data. When values repeat, multiply each value by how often it occurs, add the products, and divide by the total frequency. Suppose 3 students scored 70, 5 students scored 80, and 2 students scored 90. The average is (3 x 70 + 5 x 80 + 2 x 90) / (3 + 5 + 2) = (210 + 400 + 180) / 10 = 790 / 10 = 79. This is the weighted average formula applied to grouped data, and it saves you from writing out all ten scores.

When the Average Can Be Misleading

An average can be misleading when a dataset has an outlier — a value far away from the rest. Take the numbers 20, 22, 24, 26, and 200 again. Their average is 58.4, but four of the five values sit between 20 and 26, so 58.4 does not describe most of the data at all. The median, 24, is a much better picture of the typical value.

This is not a rare edge case. Income is the classic example: in a group where most people earn a modest salary and one person earns a great deal, the average salary looks high while the typical salary is much lower. House prices work the same way — a few very expensive homes pull the average up, which is why reports often quote the median house price instead.

The lesson is simple: whenever one extreme value changes the average a lot, compare the average with the median before you draw a conclusion. If they are close, the average is a fair summary. If they are far apart, the data is skewed, and the median is usually the more honest number.

Common Mistakes

Use this checklist before you hand in your answer:

Forgetting a value in the sum. Long lists are the danger. Add the list twice — once forward and once backward. If the two totals match, the sum is right.
Dividing by the wrong count. After adding, count the values one more time before dividing. The denominator is the number of values that went into the sum, not the number mentioned in the question.
Treating a weighted average like a plain average. Grade calculations, returns, and anywhere different items count differently — multiply by the weights first.
Mixing units before averaging. Convert everything to the same unit first. Do not add 1.5 meters to 80 centimeters and divide by 2. Convert first: 150 cm and 80 cm average to 115 cm.
Ignoring outliers. A single extreme value can pull the average far from the typical value. Check the median when the data looks skewed.
Averaging averages directly. If two groups have different sizes, their averages must be combined with weights, not simply averaged.
Expecting the average to be in the list. The average does not have to be one of your numbers. The average of 4, 7, and 9 is 6.67, which is not in the list — and that is perfectly correct.

How to Find the Average in Excel and Google Sheets

You do not need a calculator for a long list if you have a spreadsheet. In Excel or Google Sheets, put your numbers in a column — for example, cells A1 to A10 — and use the formula:

=AVERAGE(A1:A10)

Excel adds the numeric values and divides by how many numeric cells there are. Empty cells and text are ignored. For a weighted average, use:

=SUMPRODUCT(values, weights) / SUM(weights)

For example, if your values are in A1:A3 and your weights are in B1:B3, the formula is =SUMPRODUCT(A1:A3, B1:B3) / SUM(B1:B3). If you would rather check your numbers in a browser, our own Average Calculator tool on this site does the same calculation instantly, with the count, sum, median, and mode shown alongside the average.

Practice Problems

Try these, then check your answers below. Cover the answers while you work.

Find the average of 12, 18, 24, and 30.
A student scores 85, 90, 88, 92, and 95 on five quizzes. What is the average score?
The temperatures over five days are 78, 82, 79, 85, and 88 degrees. What is the average temperature?
The average of four numbers is 25. Three of the numbers are 20, 28, and 32. What is the fourth number?
An assignment worth 70 counts for 40% and an exam worth 90 counts for 60%. What is the weighted average?

Answers:

Sum = 84, count = 4, average = 21.
Sum = 450, count = 5, average = 90.
Sum = 412, count = 5, average = 82.4.
Total sum = 25 x 4 = 100. Known sum = 20 + 28 + 32 = 80. Missing number = 100 – 80 = 20.
Weighted average = (70 x 0.40) + (90 x 0.60) = 28 + 54 = 82.

If you got all five right, you have the method down. If one went wrong, work out which step failed — the sum, the count, or the division — and try it again.

Conclusion

Learning how to find the average comes down to three steps: add the numbers, count them, and divide the sum by the count. The formula is average = sum / count, and the check is that your answer must always sit between the smallest and largest values in your list. The worked examples in this guide — test scores, temperatures, prices, negative numbers, and weighted grades — all use that same method, and the practice problems give you a chance to test yourself. Just as important is knowing when the average is not enough: when an outlier pulls it away from the typical value, compare it with the median, and when some values count more than others, use a weighted average. Keep the checklist handy, use the calculator on this site to check your work, and the average will stop being a formula to memorize and start being a tool you actually use.

Frequently Asked Questions

1. What is the average formula?

The average formula is Average = Sum of all values / Number of values, also written as x-bar = (sum of x) / n. It calculates the arithmetic mean of a data set.

2. Is average the same as mean?

In everyday use, yes. Average usually means the arithmetic mean. In statistics, average is a broader term that also covers the median and the mode, which are different measures of what is typical.

3. How do you calculate the average?

Add all the numbers together to get the sum, count how many numbers there are, then divide the sum by the count. For example, the average of 5, 10, and 15 is (5 + 10 + 15) / 3 = 10.

4. What is the difference between mean and median?

The mean is the sum divided by the count, and it uses every value. The median is the middle value when the numbers are sorted. The mean is pulled by outliers; the median is not, so the median is often better for skewed data like income.

5. Can the average be a decimal even if all values are whole numbers?

Yes. For example, the average of 4, 7, and 9 is 20 / 3 = 6.67. The average is rarely a whole number unless the values divide evenly.

6. Can the average be larger than the largest value, or smaller than the smallest?

No. The arithmetic mean of any data set always lies between the minimum and the maximum. If your computed average lies outside that range, you made an error in adding or counting.

7. How do I find the average of grades?

If every grade counts equally, add the grades and divide by how many there are. If they have different weights — for example, an exam worth 50% and homework worth 20% — multiply each grade by its weight, add the products, and divide by the total weight.

8. How do I calculate a weighted average?

Multiply each value by its weight, add those products together, and divide by the total weight. If the weights are percentages that total 100%, you can multiply each value by its decimal weight and add the results.

9. What is the average of 10, 20, and 30?

The average of 10, 20, and 30 is (10 + 20 + 30) / 3 = 60 / 3 = 20.

10. How do you find the average in Excel?

Put your numbers in a column, for example cells A1 to A10, and use the formula =AVERAGE(A1:A10). Excel adds the numeric values and divides by how many numeric cells there are.

Sources

Further reading: Try our Average Calculator tool, browse more posts in News, learn more About Us, or Contact Us.

How to Find the Average: A Simple Step-by-Step Guide