Grade & GPA · Guide
How to Find the Average of Numbers
Add them up, then divide by how many there are. That is the whole idea — here is how to use it without slipping.
Want the answer for your own numbers? Use the free Average Grade Calculator — it does every step below for you.
What is an average?
An average is one number that represents a whole group. In everyday use, "average" means the mean: the total shared out equally. If five friends spend $10, $15, $20, $25 and $30, the average is what each would have spent if they had all paid the same — $20.
How to find the average in two steps
- Add all the numbers together.
- Divide the total by how many numbers there are.
Average = sum of the values ÷ number of values
Example: test scores
Scores: 78, 85, 92, 70, 88, 91.
Sum: 78 + 85 + 92 + 70 + 88 + 91 = 504. There are 6 scores.
504 ÷ 6 = 84
Averages with decimals, negatives and zeros
- Decimals: 2.5, 3.1 and 4.0 add up to 9.6. 9.6 ÷ 3 = 3.2.
- Negative numbers: temperatures of −4, 2, 5 and −1 add up to 2. 2 ÷ 4 = 0.5.
- Zeros count. A missed assignment scored 0 is still one of the values. Scores of 90, 80 and 0 average 56.7, not 85.
Weighted average: when some numbers count more
If items have different importance, multiply each by its weight, add, and divide by the total weight.
Example: a course grade
Homework 90 (weight 20%), midterm 75 (30%), final 85 (50%).
(90 × 0.2) + (75 × 0.3) + (85 × 0.5) = 18 + 22.5 + 42.5.
Weighted average = 83
A plain average of the three would give 83.3 — close here, but often very different. Our guide to weighted grades goes deeper.
Averaging percentages and averages
Only average percentages directly when each one is out of the same total. If you scored 9/10 on one quiz and 30/50 on a test, the percentages are 90% and 60%, but the true overall score is 39/60 = 65%, not 75%. Add the raw marks first.
The same goes for averaging two class averages. A class of 10 averaging 80 and a class of 30 averaging 70 have a combined average of (800 + 2,100) ÷ 40 = 72.5, not 75.
Finding the score you need
Averages also work backwards. If you know the average you want, you can find the missing number:
Score needed = target average × total number of scores − sum so far
Example: scores of 78, 85 and 92, and you want an 85 average over four tests
Target total: 85 × 4 = 340. Sum so far: 78 + 85 + 92 = 255.
You need 340 − 255 = 85 on the fourth test
When some tests count more than others, use the final grade calculator instead.
The average speed trap
Drive somewhere at 60 mph and back at 40 mph. The average speed is not 50 mph. You spend longer on the slow leg, so it counts for more. Over the same distance each way, the answer is:
Average speed = 2 ÷ (1/60 + 1/40) = 48 mph
For any trip, the safe method is total distance ÷ total time.
Moving averages
A moving average smooths out bumpy data. A three-month moving average takes the latest three months, averages them, then slides forward one month at a time. Sales of 100, 120, 110 and 140 give three-month averages of 110 (first three) and 123.3 (last three). It shows the trend without the month-to-month noise.
Average in a spreadsheet
In Excel or Google Sheets, type =AVERAGE(A1:A10). For a weighted average, use =SUMPRODUCT(scores, weights)/SUM(weights).
Mean, median and mode
The mean is not the only kind of average. The median is the middle value once sorted, and the mode is the most common value. When one number is extreme — like a single huge salary — the median often describes the group better. The median calculator gives all three at once.
Frequently asked questions
Add all the numbers together, then divide by how many numbers there are. For 78, 85, 92, 70, 88 and 91, the total is 504 and there are 6 numbers, so the average is 84.
Multiply each value by its weight, add the results, and divide by the total of the weights. Scores of 90, 75 and 85 weighted 20%, 30% and 50% give a weighted average of 83.
Yes. A zero is a real value and must be included in both the sum and the count. Leaving it out makes the average look higher than it is.
Multiply your target average by the total number of scores, then subtract the scores you already have. With 78, 85 and 92, an average of 85 over four tests needs 85 × 4 − 255 = 85 on the last one.
Because you spend more time at the slower speed. At 60 mph out and 40 mph back over the same distance, the true average is 48 mph. Always divide total distance by total time.