Key takeaways
- Average (mean) = sum of the numbers ÷ how many numbers there are.
- For three numbers: (a + b + c) ÷ 3.
- A zero still counts. Include it in the sum and in the count.
- One extreme value can pull the mean far away from the typical value.
In this guide
What is the average?
Imagine you pour all the numbers into one pot and then share the total out equally. The amount each one gets is the average. If three friends have 4, 6 and 8 sweets and they share them fairly, each gets 6. So 6 is the average.
In maths, this kind of average is called the mean. This calculator finds the mean of three numbers, but the same idea works for any amount of numbers.
Why does the average matter?
A long list of numbers is hard to understand at a glance. The average squeezes the whole list into one typical value. That makes comparisons easy: this month vs last month, your class vs another class, one shop's prices vs another's.
It is also the starting point for almost every other idea in statistics. Spread, standard deviation and z-scores are all measured from the mean.
The mean does not have to be one of your numbers. The average of 72, 85 and 90 is about 82.33, a score nobody actually got.
The formula
| Symbol | What it means | Example |
|---|---|---|
| a | The first number | 72 |
| b | The second number | 85 |
| c | The third number | 90 |
| ÷ 3 | Divide by the count (3 numbers) | 247 ÷ 3 |
The answer has the same unit as your numbers. The average of three prices in dollars is a price in dollars. With five numbers, you would divide by 5 instead of 3.
How to find the average step by step
- 1Write down all the numbers. Make sure they use the same unit.
- 2Add them together. This total is the sum.
- 3Count the numbers. Zeros count too.
- 4Divide the sum by the count. The result is the average.
Now type your own three numbers into the calculator below and see every step worked out.
Try it yourself
Pre-filled with the example — change any value.
Common mistakes to avoid
- Skipping zeros. A test score of 0 is still a score. Leaving it out makes the average look better than it is.
- Mixing units. Do not average 2 metres with 150 centimetres. Change them to the same unit first.
- Trusting the mean when there is an extreme value. For 1, 2, 3, 4 and 100 the mean is 22, which is not typical of the list at all. The median calculator gives a fairer middle value here.
- Rounding too early. Keep the full sum and round only the final answer.
Tips and tricks
- Estimate first. The average always sits between the smallest and largest number. For 72, 85 and 90, an answer below 72 or above 90 must be wrong.
- Some values matter more? If an exam counts more than homework, use the weighted average calculator.
- Want to know how spread out the numbers are? Try the standard deviation calculator.
Where you'll use it in real life
- School: your average test mark or your average homework time per day.
- Money: your average monthly spending on food or phone bills.
- Travel: average speed on a trip, or average fuel used per week.
- Weather and sport: average rainfall in a month, or a player's average runs or goals per game.
Quick summary
To find the average, add all the numbers and divide by how many there are. Check that your answer sits between the smallest and largest value, and switch to the median when one number is extreme. Use the calculator above to get the average of three numbers with every step shown.
Worked example
You took three maths tests this term and scored 72, 85 and 90. You want one number that shows how you did overall.
- 01Average = (72 + 85 + 90) ÷ 3
- 02Average = 247 ÷ 3
- 03Average = 82.33
These numbers are pre-filled in the calculator above.
Frequently asked questions
Is the average the same as the mean?
Yes. In everyday language, average usually means the arithmetic mean: add the numbers and divide by how many there are. The median and mode are other kinds of middle, but they are not the mean.
How do I find the average of more than three numbers?
Add all of them and divide by how many there are. For 2, 4, 6 and 8 the sum is 20 and there are 4 numbers, so the average is 20 ÷ 4 = 5.
Can the average be a decimal?
Yes. The average of 72, 85 and 90 is 247 ÷ 3 ≈ 82.33, even though every score was a whole number.
What score do I need to reach a target average?
Multiply the target average by the total number of tests, then subtract the marks you already have. For an average of 80 over 3 tests, you need 240 in total.
