Average and Weighted Average Calculator
Paste your grades or values and get the average, median, mode and standard deviation. With weights, calculate the weighted average or the grade needed to finish the year.
Educational use: results are estimates made for study and reference. Checking the answer and deciding what to do with it is the sole responsibility of whoever uses the tool. Read the legal notice.
On this page
- How to use the calculator
- The formulas
- Worked examples
- Mean and median on a number line
- Common mistakes with averages
- When to use each measure
- About your school's rules
- Questions about averages
- Where the average comes from
- Where averages show up
- Statistical curiosities
- Basic statistics vocabulary
- Everyday tools
How to use the calculator
Simple average and statistics
Choose the first option and type the values, one per line or separated by spaces. You get the average, the sum, the median, the mode, the smallest and largest values and two kinds of standard deviation.
Weighted average
Choose the second option and type one "value weight" pair per line. If one test counts double compared to another, the first has weight 2 and the second has weight 1. If you leave out the weight, the tool assumes 1.
Needed grade
In the third option, enter the grades already recorded with their weights, the average you want to reach, the weight of the next test and, if you like, the maximum grade. The tool calculates what you need to score and tells you when the target is already secured or has become impossible.
Typing decimals: a period and a comma both work. To separate values, use a space, a line break or a semicolon.
The formulas
Arithmetic mean
Weighted average
Median and mode
- Median: the middle value when the numbers are put in order. If the count is even, it is the average of the two middle values.
- Mode: the value that appears most often. There can be more than one, or none.
Standard deviation
s = √[ Σ(xᵢ − average)² ÷ (n − 1) ] (sample)measures how far the values spread from the average
The population standard deviation is for when you have all the data (every grade in the class). The sample standard deviation is for when your data is a sample of a larger group (a survey of 100 people, from an entire city).
Needed grade
The formula comes straight from the definition of the weighted average: set up the equation with x as the unknown and solve for x.
Worked examples
1. Simple average of three grades
2. Weighted average
One test with weight 2 (grade 8) and another with weight 3 (grade 6).
Notice that the simple average would be 7, but since the test with the lower grade counts more, the weighted average comes out lower.
3. What do I need to score?
Grades so far: 6 (weight 2) and 7 (weight 3). The next test has weight 5 and the target average is 7.
You need to score 7.4 on the next test.
4. Mean versus median
Values: 1, 2, 3 and 10.
The 10 pulls the average up, but the median still describes the "typical value" well. When there are values far outside the pattern, the median is more reliable.
5. Standard deviation
Values: 2, 4, 4, 4, 5, 5, 7 and 9.
Mean and median on a number line
Placing the numbers on a line helps you see the difference between the mean and the median. The balance point of the mean is pulled by extreme values, while the median sits in the middle of the line-up.
Common mistakes with averages
Using a simple average when the weights differ
If the tests have different weights, the simple average is misleading. Check the course rules to see how much each assessment is worth.
Forgetting to divide by the sum of the weights
In a weighted average, you divide by the sum of the weights, not by the number of grades. With grades 8 (weight 2) and 6 (weight 3), the divisor is 5, not 2.
Averaging averages
The average of the averages of groups of different sizes is not the overall average. A class of 10 students with an average of 8 and another of 30 with an average of 6 give an overall average of 6.5, not 7.
Trusting the average when there are extreme values
With salaries, prices and times, one very high value distorts the average. The median shows better what is typical.
Mixing commas and periods
"7,5" and "7.5" are the same value here, but "1.500" will be read as 1.5. Write large numbers without a thousands separator.
When to use each measure
| Measure | Answers... | Watch out |
|---|---|---|
| Arithmetic mean | what is the "average" or balance value? | sensitive to extreme values |
| Weighted average | what is the average when items have different importance? | depends on correct weights |
| Median | what is the middle value of the line-up? | ignores the distance between values |
| Mode | what is the most common value? | may not exist, or there may be several |
| Standard deviation | are the values clustered or spread out? | only makes sense alongside the mean |
| Minimum and maximum | what is the range of the data? | a single outlier changes everything |
Two sets can have the same mean and be completely different: 5, 5, 5, 5 and 1, 3, 7, 9 both have a mean of 5, but the second is much more spread out. The standard deviation captures that difference.
About your school's rules
The tool calculates averages exactly from the numbers you type. What it does not know are the rules of your school, college or company: rounding (up, down, to the nearest whole number), make-up grades, minimum averages per subject, passing criteria and grade replacement vary a lot.
The needed-grade result is mathematical and assumes the weights you entered are correct. For decisions that affect passing, scholarships or evaluations, always confirm with the institution's official rules.
Bottom line: this tool is educational. Results do not replace your own checking, and how you use them is entirely your responsibility. More details in the legal notice.
Questions about averages
How do I calculate the average of grades?
Add up all the grades and divide by the count. With 7, 8.5 and 9: 24.5 ÷ 3 ≈ 8.17.
What is a weighted average?
It is an average in which each value has a different weight. You multiply each value by its weight, add up the results and divide by the sum of the weights.
How do I calculate the grade I need to pass?
Use the "What grade I need on the next test" option, entering the grades already recorded with their weights, the target average and the weight of the next assessment.
What is the difference between mean and median?
The mean is the sum divided by the count. The median is the middle value of the data in order. With extreme values, the two can differ a lot.
What is the mode?
It is the value that appears most often in a set. In 2, 3, 3, 5 and 7, the mode is 3. There may be no mode, or more than one.
Which standard deviation should I use, population or sample?
Use the population one when you have all the data for the group you want to describe. Use the sample one when your data is a sample of a larger group.
Can I use decimal weights?
Yes. Weights such as 0.3 and 0.7 work normally, and dividing by the sum of the weights adjusts everything.
What if I forget to enter the weight?
The tool assumes a weight of 1 for the line with no weight. In a list with no weights, this is the same as the simple average.
Why does the tool say the target is unreachable?
Because even with the maximum grade on the next assessment, the target average would not be reached. Check that the maximum grade is correct (default: 10).
How many values can I type?
Many. The tool handles hundreds of values with no problem, as long as they are separated by spaces, line breaks or semicolons.
Where the average comes from
The idea of taking a "typical" value among many is ancient, and the word "average" suggests the middle, the balance point. Ancient astronomers already combined several measurements of the same phenomenon into one, trusting that errors above and below would cancel out.
In the 19th century, Carl Friedrich Gauss linked the behavior of measurement errors to a bell-shaped curve, the normal distribution, and showed why the mean is a good estimate. The term "standard deviation" was popularized by the statistician Karl Pearson, in 1894.
Where averages show up
- School and college: grade averages, weights of tests and assignments, the grade needed to pass.
- Sports: average points per game, time per lap and speed.
- News and surveys: "the average age", "the average waiting time".
- Usage tracking: average water, electricity and fuel consumption per period.
- Science and lab work: averaging repeated measurements and estimating the error with the standard deviation.
- Work: targets, indicators and team performance.
Statistical curiosities
- The average family can have 1.9 children, and no real family has 1.9 children. The average is a descriptive tool, and it does not have to match a real case.
- Simpson's paradox. A treatment can be better in each separate group and worse overall, when the groups have very different sizes. Overall averages can hide what happens inside the groups.
- Three classic means: arithmetic, geometric and harmonic, known since the Pythagoreans. Each is the right one for a certain type of problem, and the harmonic mean, for example, is the one that works for speeds over legs of the same distance.
Basic statistics vocabulary
- Arithmetic mean
- The sum of the values divided by how many there are.
- Weight
- A number that indicates the importance of a value in the weighted average.
- Median
- The central value of an ordered set.
- Mode
- The value that appears most frequently.
- Standard deviation
- A measure of how far the values typically spread from the mean.
- Variance
- The square of the standard deviation. It measures spread in squared units.
- Outlier
- A value far from the others, which can distort the average.