IIf you need to calculate an average, the basic formula is simple:
[
\boxed{\text{Average}=\frac{\text{Sum of all values}}{\text{Number of values}}}
]
For example, the average of 10, 20, 30, and 40 is:
\frac{100}{4}
25
]
The average is 25.
In mathematics, this is called the arithmetic mean. It is the most common type of average used for test scores, grades, marks, class results, and everyday numerical data.
How to Calculate an Average
You only need three steps:
- Add all the numbers.
- Count how many numbers there are.
- Divide the total by the number of values.
Example
Find the average of:
70, 75, 80, 85, 90
Add the values:
[
70+75+80+85+90=400
]
There are 5 values:
[
400\div5=80
]
Average = 80
Average Formula
The standard formula is:
[
\boxed{\bar{x}=\frac{\sum x}{n}}
]
Where:
- (\bar{x}) = average
- (\sum x) = sum of all values
- (n) = number of values
So whenever you’re unsure how to find an average, remember:
Add → Count → Divide.
How to Calculate the Average of Two Numbers
To find the average of two numbers, add them together and divide by 2:
[
\boxed{\text{Average}=\frac{a+b}{2}}
]
Example
What is the average of 60 and 80?
\frac{140}{2}
70
]
Answer: 70
Another example:
[
\frac{75+95}{2}=85
]
So the average of 75 and 95 is 85.
For two numbers, the average is also the midpoint between them.
How to Calculate the Average of Multiple Numbers
The same formula works whether you have three numbers or hundreds.
For example:
12, 18, 25, 30, 35
First add them:
[
12+18+25+30+35=120
]
Then count them:
[
n=5
]
Now divide:
[
120\div5=24
]
Average = 24
What if a number appears more than once?
Every occurrence counts.
For example:
10, 10, 20, 30
There are four values, not three.
[
\frac{10+10+20+30}{4}=17.5
]
Average = 17.5
How Does a Grader Calculate the Class Average?
If you’re asking how a teacher or grader calculates the average score for a class, the usual method is to add the included student scores and divide by the number of scores.
\frac{\text{Total Student Scores}}
{\text{Number of Students}}
}
]
Example
Five students receive these scores:
| Student | Score |
|---|---|
| A | 70 |
| B | 75 |
| C | 80 |
| D | 85 |
| E | 90 |
Add the scores:
[
70+75+80+85+90=400
]
Divide by 5 students:
[
400\div5=80
]
Class average = 80%
That’s the simple arithmetic mean of the students’ scores.
Class Average vs. Your Class Grade
These two calculations are easy to confuse.
A class average describes the performance of a group of students.
Your individual class grade describes your own performance and may be calculated from points, percentages, assignment categories, or weights.
For example, if your course uses a points-based system, your grade may be calculated as:
[
\frac{\text{Points Earned}}{\text{Points Possible}}\times100
]
If you want to understand that separate calculation, see our guide on how to calculate grades in class.
How to Calculate an Average Grade
If every grade has equal importance, calculate the simple average.
Suppose your grades are:
- 80%
- 75%
- 90%
- 85%
Add them:
[
80+75+90+85=330
]
Divide by 4:
[
330\div4=82.5
]
Average grade = 82.5%
However, if your assignments have different weights, a simple average may not be the correct way to calculate your final grade.
How to Calculate a Weighted Average
A weighted average is used when some values have more importance than others.
For grades, this commonly happens when:
- homework is worth 20%
- quizzes are worth 20%
- midterms are worth 25%
- the final exam is worth 35%
The formula is:
\frac{\sum(\text{Score}\times\text{Weight})}
{\sum\text{Weights}}
}
]
Example
Suppose your grades are:
| Category | Score | Weight |
| Homework | 90% | 20% |
| Quizzes | 80% | 30% |
| Exams | 85% | 50% |
Calculate each contribution:
[
90\times0.20=18
]
[
80\times0.30=24
]
[
85\times0.50=42.5
]
Add them:
[
18+24+42.5=84.5
]
Weighted average = 84.5%
A simple average would be:
[
(90+80+85)\div3=85%
]
The results differ because the categories don’t have equal weights.
If you’re calculating a course grade with different assignment weights, use the Weighted Grade Calculator to calculate the overall weighted result.
Simple Average vs. Weighted Average
The easiest question to ask is:
Does every value count equally?
If yes, use a simple average.
If no, use a weighted average.
Simple average
Use it when every value has equal importance.
Example:
- Quiz 1 = 80
- Quiz 2 = 90
- Quiz 3 = 70
[
(80+90+70)\div3=80
]
Weighted average
Use it when different values have different importance.
For example, if a final exam is worth 50% of the course grade, it should have more influence than a homework category worth 10%.
How to Calculate an Average Percentage
If all percentages have equal importance, add them and divide by the number of percentages.
Example:
70%, 80%, 90%, 100%
[
70+80+90+100=340
]
[
340\div4=85
]
Average percentage = 85%
Be Careful When Averaging Percentages
Simply averaging percentages is not always appropriate.
For example:
- Test A: 90% on 10 questions
- Test B: 70% on 100 questions
A simple average gives:
[
(90+70)\div2=80%
]
But the two tests contain different numbers of questions.
If every question should have equal importance, you should calculate the combined result from the underlying points instead.
How to Calculate Average Marks
If each assessment has equal importance, add the marks and divide by the number of assessments.
Suppose your marks are:
65, 72, 80, 83, 90
[
65+72+80+83+90=390
]
There are five scores:
[
390\div5=78
]
Average marks = 78
If the assessments have different weights or maximum marks, the correct calculation may be different.
How to Calculate an Average Test Score
Suppose you have three test scores:
- Test 1 = 72
- Test 2 = 84
- Test 3 = 90
Add them:
[
72+84+90=246
]
Divide by 3:
[
246\div3=82
]
Average test score = 82
If you’re averaging several quiz results, you can use the Quiz Score Calculator. It supports multiple quiz scores and can also account for a drop-lowest policy or different quiz weights.
What Happens If You Get a Zero?
A real zero should normally be included in the average.
For example:
80, 90, 0
[
\frac{80+90+0}{3}=56.67
]
Average = 56.67
But a blank or missing score isn’t automatically a zero.
If an assignment hasn’t been graded yet, whether it counts as zero depends on your teacher’s grading policy.
This distinction can make a significant difference to a student’s current average.
How to Calculate an Average With Negative Numbers
Negative numbers are included normally.
Example:
-10, 20, 30
[
-10+20+30=40
]
There are three values:
[
40\div3=13.33
]
Average ≈ 13.33
The negative sign must be included when adding the numbers.
How to Calculate an Average With Decimals
Decimals don’t change the formula.
Example:
2.5, 3.5, 4.0
[
2.5+3.5+4=10
]
[
10\div3=3.333…
]
Average ≈ 3.33
It’s generally better to keep full precision while calculating and round the final answer.
How to Find a Missing Number From an Average
You can also work backward when the average is known.
Suppose four numbers have an average of 25:
20, 30, 15, x
First find the total required:
[
25\times4=100
]
Add the known values:
[
20+30+15=65
]
Subtract:
[
100-65=35
]
Therefore:
[
\boxed{x=35}
]
The general formula is:
(\text{Average}\times\text{Number of Values})
\text{Known Total}
}
]
This is useful when solving homework questions where the average and all but one value are given.
How to Calculate a Combined Average
You need to be careful when combining two averages.
Suppose:
- Group A has 10 students with an average of 70
- Group B has 30 students with an average of 80
You cannot simply do:
[
(70+80)\div2=75
]
because the groups aren’t the same size.
Instead, calculate the total represented by each group:
[
10\times70=700
]
[
30\times80=2400
]
Combined total:
[
700+2400=3100
]
Combined number of students:
[
10+30=40
]
Now divide:
[
3100\div40=77.5
]
Combined average = 77.5
Can You Average Two Averages?
Yes, but not always by simply adding them and dividing by two.
If both groups have the same number of observations, a simple average of the two group averages works.
If the groups have different sizes, use their group sizes as weights.
\frac{(\text{Average}_1\times n_1)+(\text{Average}_2\times n_2)}
{n_1+n_2}
}
]
This is particularly useful for combining class averages, survey groups, or test results from different groups.
Mean vs. Average: Are They the Same?
In basic mathematics, average usually means the arithmetic mean.
The arithmetic mean is:
[
\frac{\text{Sum of Values}}{\text{Number of Values}}
]
But statistics has several ways of describing the center of a data set.
The most common are:
- Mean
- Median
- Mode
These should not be confused with one another.
Mean vs. Median vs. Mode
Consider:
10, 12, 12, 15, 50
Mean
[
\frac{10+12+12+15+50}{5}=19.8
]
Median
After sorting the numbers, the middle value is:
12
Mode
The value that occurs most often is:
12
So:
- Mean = 19.8
- Median = 12
- Mode = 12
The high value of 50 pulls the mean upward.
If you’re learning statistics, understanding mean vs. median vs. mode can help you decide which measure best represents your data.
Can an Outlier Change the Average?
Yes.
Consider these scores:
70, 72, 74, 76, 78
Their average is:
[
74
]
Now replace 78 with 200:
70, 72, 74, 76, 200
The new average is:
[
98.4
]
One unusually high value has changed the mean substantially.
This is why the mean can sometimes be less representative when a data set contains extreme values.
What Does a Class Average Tell You?
A class average gives you a single summary of student performance.
For example, a class average of 80% means the arithmetic mean of the included scores is 80%.
But it doesn’t tell you how those scores are distributed.
Two classes could both have an 80% average:
Class A
78, 79, 80, 81, 82
Class B
50, 60, 80, 100, 110
The averages are the same, but the score distributions are very different.
For a fuller picture, teachers may also consider:
- median
- highest score
- lowest score
- range
- standard deviation
- score distribution
Common Mistakes When Calculating an Average
1. Dividing by the wrong number
If there are 5 values, divide by 5.
2. Forgetting repeated values
Every occurrence counts.
3. Treating a blank as zero
A missing value isn’t necessarily a zero.
4. Ignoring grade weights
A final exam worth 40% should not be treated the same as homework worth 10%.
5. Averaging group averages directly
Different-sized groups need a combined weighted calculation.
6. Rounding too early
Keep enough precision until the final answer.
7. Confusing average score with final course grade
A class average and an individual weighted course grade can be completely different calculations.
Average Formula Cheat Sheet
| What You Need | Formula |
| Average of numbers | Sum ÷ Count |
| Average of two numbers | (a + b) ÷ 2 |
| Class average | Total scores ÷ Number of scores |
| Weighted average | Σ(score × weight) ÷ Σweights |
| Missing value | Average × Count − Known Total |
| Combined average | Combined Total ÷ Combined Count |
Frequently Asked Questions
How do you calculate an average?
Add all the values and divide the total by the number of values.
[
\text{Average}=\frac{\text{Sum}}{\text{Count}}
]
How do you calculate the average of two numbers?
Add the two numbers and divide by 2.
For example:
[
(20+40)\div2=30
]
How does a grader calculate a class average?
For equally weighted scores, the grader adds the included student scores and divides by the number of students or scores.
How do you calculate an average grade?
If all grades have equal weight, add them and divide by the number of grades. If they have different weights, use a weighted average.
Is average the same as mean?
Usually, when people say “average” in basic mathematics, they mean the arithmetic mean.
Can an average be a decimal?
Yes. An average doesn’t have to be a whole number.
Can an average be negative?
Yes. If the total of the values is negative, the arithmetic mean can also be negative.
Should zero be included in an average?
Yes, if zero is an actual value or score. A blank entry isn’t automatically a zero.
Can you average two averages?
Yes, but if the groups have different sizes, use a weighted combined average rather than simply averaging the two means.
What is a weighted average?
A weighted average gives different values different levels of importance. It is commonly used for course grades and assignments with different percentage weights.
Calculate Your Average Faster
For a small set of numbers, remember:
Add → Count → Divide.
If you’re working with several quiz scores, the Quiz Score Calculator can calculate the quiz average and handle options such as dropped-lowest scores and different quiz weights.
If your course uses different assignment weights, the Weighted Grade Calculator can calculate your overall weighted course grade.
If you’re trying to determine the score you need on an upcoming final exam, use the Final Grade Calculator to work backward from your target grade.
For a single test or quiz, the Easy Grade Calculator can calculate the percentage and letter grade from your score.
Final Answer
The basic formula for calculating an average is:
[
\boxed{\text{Average}=\frac{\text{Sum of all values}}{\text{Number of values}}}
]
For two numbers, add them and divide by 2.
For a class average, add the included student scores and divide by the number of scores.
For weighted grades, multiply each score by its weight before combining the results.
The most important part is choosing the right method. A simple average works when values count equally; a weighted average is needed when some values have greater importance.