A number set may have more than one valuable piece of information in it. The average will provide you the overall numerical center, the median will give you the middle number, and the range will tell you about the difference between the smallest and the largest number. Looking at all these pieces of information in one place is more informative than the basic calculator, which provides one output at a time.
How to Calculate the Average
For calculation of the average for a group of numbers:
- Add up all the numbers.
- Count the number of values present.
- Divide their sum by the number of values.
The arithmetic mean formula is:
The same formula can also be written with summation notation:
For example, suppose the numbers are 12, 18, 24, and 30:
The arithmetic mean is 21. This straightforward formula solves some common questions like “How do I calculate an average?” and “How can I find the average of few numbers?”
How to Use This Tool
Insert your values in the data set. You can use either a comma or space to separate the numbers, as follows:
10, 20, 30, 40, 50, 15, 25, 35
The result will automatically display as you insert the data without pressing a “calculate” button. You can:
- Click on “Copy” to copy the result onto the clipboard.
- Click on “Save” to save the result as an image.
- Click on “Reset” to remove the existing data and start a fresh calculation.
Whole numbers and decimals, as well as negative numbers can be used for arithmetic operations in the tool. However, the geometric mean can be calculated only if all the values are positive.
Example Calculation
Look at the following data set that is also given in the tool:
10, 20, 30, 40, 50, 15, 25, 35
The tool produces these results:
| Result | Value |
| Arithmetic mean | 28.13 |
| Sum | 225.00 |
| Count | 8 |
| Median | 27.50 |
| Geometric mean | 25.10 |
| Largest value | 50 |
| Smallest value | 10 |
| Range | 40 |
The exact arithmetic mean without rounding is:
It is rounded to two decimal places, and the tool displays 28.13.
To calculate the median, you need to put the numbers in order from smallest to largest:
10, 15, 20, 25, 30, 35, 40, 50
Since there are eight numbers in the list, the median will be the average of the two middle numbers, 25 and 30:
What Each Result Means
Arithmetic Mean
The “arithmetic mean” is the result that everyone is looking for when he uses an average number calculator or mean calculator. The arithmetic mean is the sum of the values divided by the number of values, where all the values play the same role in the result.
This statistic is useful in the case of equal-weight data: exam scores, daily temperatures, sales, costs, etc. However, one very large or very small number may distort the result from the typical value.
Sum
The sum is the sum of all valid numbers:
It is easier to see how sum helps to calculate the result since it shows the value that is divided by the count.
Count
“Count” indicates the number of valid numeric entries in the formula used for calculations. The count becomes the denominator for the computation of the arithmetic mean.
The count can also help in spotting missing and incorrectly entered data. For instance, in case you want to enter 12 data entries but the count shows 11, it means that either there is some missing information or one of the entries is not entered in the right format.
Median
The “median” refers to the middle number obtained once the values are ordered in ascending order.
In case the number of the data entries is odd, the middle number is referred to as the median. In case the number of the data entries is even, then the median is obtained by averaging the two middle numbers.
The median is a better measure of central tendency than the arithmetic mean in case there is an outlier. One extremely high salary, home price, and transaction value may alter the mean considerably but will hardly affect the median.
Geometric Mean
The geometric mean can be calculated by multiplying all the numbers together and then taking an nth root of the resulting product:
Such a measure works well for proportional or multiplicative values. Typical examples are growth rates, returns on investment, ratios, percent changes, etc.
A typical geometric mean calculation assumes that the values are positive. For ordinary additive values, such as expenditures, scores, and measurements, the arithmetic mean is often a better choice.
Largest and Smallest Values
The maximum is the highest value in the set, whereas the minimum is the lowest.
These two measures help determine the bounds of your data instantly without having to sort the data set yourself.
Range
The range describes the whole span from the maximum value to the minimum one:
If we have a set with the minimum of 10 and the maximum of 50, the range is:
The range equals 40. The bigger the range is, the greater span of data is covered, but the range itself doesn’t say anything about the distribution of values within this span.
Mean vs. Median: Which Result Should You Use?
The arithmetic mean is recommended to be used if all observations are supposed to be of equal importance and no outliers are present in the data.
The median measure can be used when you need the middle value of observations or when some observations are unusually high or low and can make the arithmetic mean less representative.
Take a look at these sales figures by month:
8,000, 8,500, 9,000, 9,500, 60,000
The arithmetic mean is:
The median is 9,000.
These two measures are both mathematically correct, but they describe the set of data in different ways. The arithmetic mean takes into account the presence of the outlier figure, whereas the median is closer to four other figures.
Can This Be Used as a Grade Average Calculator?
Sure, you can use the calculator to find the arithmetic average if all figures are equally important and have the same weight.
For scores of 78, 84, 91, and 87:
The grade average is 85.
This is what makes the tool helpful in calculating the average of a test, the average of an exam, a grade calculator, or a basic calculator.
But most courses have varying percentages allocated to the performance in homework, quizzes, projects, midterms, and the final examination. In this case, you will require a weighted calculation and not an arithmetic mean.
Such as:
- Homework score: 90 with 20% weightage
- Midterm score: 80 with 30% weightage
- Final exam score: 88 with 50% weightage
The correct weighted grade is:
Inputting 90, 80, and 88 as equally important numbers will give a different answer, as the input percentages will be neglected.
The calculation of GPA can also be based on credit hours, conversions to letter grades, the particular scale of the institution, among others. This is why you should use the tool only as an estimation tool of GPA and not a GPA calculator.
Can It Calculate an Average Percentage?
Yes, you can use it to calculate the average percentage when all percentages are equal in significance and have similar data bases.
For 75%, 80%, and 90% percentages:
Type in the numbers without percent signs:
75, 80, 90
The obtained average will be 81.67%.
A simple percentage average cannot be used when the percentages are derived from different numbers of items/groups/assessments.
For instance:
- 90% for a quiz having 10 questions
- 60% for an exam having 100 questions
The standard average for the two percentages will be 75%, which means both assessments are equally important. To obtain the combined score correctly, you need to use the raw numbers:
It is necessary to apply a weighted procedure if percentages are of different point totals, denominators, credits, samples, or weights.
How to Calculate an Average in Excel or Google Sheets
To calculate an average in MS Excel, fill the cells with data in a row or column and then use the following formula:
=AVERAGE(A1:A10)
The function AVERAGE finds the arithmetic mean of all numbers in the range. There are also AVERAGEIF and AVERAGEIFS functions that can be used in case there is a need to find results with one or several conditions.
The same formula is used for calculations in Google Sheets:
=AVERAGE(A1:A10)
However, in Google Sheets there are special functions to find a median, geometric mean, mode, and weighted results.
This online calculator is very useful if there is no time to open a table and write a formula.
How to Calculate the Average of Two Numbers
Add the two values and divide the result by two:
For 18 and 26:
The arithmetic mean is 22.
How to Calculate the Average of Three Numbers
Add the three values and divide the total by three:
For 12, 15, and 21:
The arithmetic mean is 16.
How to Calculate an Average of Averages
Calculating an Average of Averages
A straight mean average of several group averages is a true reflection only if all the groups have equal numbers of data points.
For example, the first class has:
- Mean score of 90
- The number of students is 10.
The second class has:
- Mean score of 70
- The number of students is 30
The mean of 90 and 70 is 80; however, this answer wrongly assumes that the two classes have an equal number of students.
The proper calculation for this situation would be:
If groups have unequal sizes, multiply the mean of each group by its number of data points, then sum the results and divide by the total number of observations.
When a Special Calculation Is Needed
Just because there is the word “average” in your search does not mean that it is just an ordinary arithmetic mean. Here is how to know which one is appropriate.
| If your need is | Is this tool suitable? | Correct approach |
| Grade average calculator | Yes, for grades that carry the same weight | Sum up all grades, then divide by the number of grades |
| Weighted average calculator | No | Multiply value with its corresponding weight |
| Average percentage calculator | Yes, in case percentages carry the same weight | Calculate arithmetic mean |
| Stock average calculator | Only when the number of stocks is equal | Weight the purchase price with the number of stocks |
| Batting average calculator | No, from individual game percentages | Total hits divided by total at bats |
| Average speed calculator | No, from unconnected speed measurements | Distance traveled divided by total time |
| Average velocity calculator | No | Divide displacement by elapsed time |
| Average atomic mass calculator | No | Weight each isotope by its natural abundance |
| Average and standard deviation calculator | No | Use statistics calculator, including standard deviation |
| Average median mode calculator | Partly | Partially This calculator gives the average and median, not the mode. |
Stock Prices and Share Purchases
It is only possible to calculate the mean of prices accurately when the same quantity of shares is bought at each price.
When different amounts are bought at each price, it is necessary to compute the weighted average price per share:
For example, say you have purchased 10 shares for $20 and 30 shares for $30:
The weighted average price will be $27.50 per share. When one simply enters 20 and 30, one gets 25, which is incorrect. Other factors that affect the actual cost of buying stocks are commissions, taxes, exchange rates, and stock splits.
Batting Average
The average batting rate of a baseball player is calculated using the total hits divided by the total number of at-bats rather than the arithmetic mean of several percentages obtained in a game:
If a player has 25 hits in 100 at-bats, then his batting average is:
Average Speed and Velocity
Average speed is calculated by dividing the total distance covered by the total time taken:
Average velocity is calculated by dividing displacement by the total time:
When simply adding several speeds together gives a misleading result because of unequal time periods between readings.
Average Atomic Mass
The average atomic mass is a weight average based on the mass and natural abundance of each isotope:
As the amount of isotopes in nature is different from each other, a simple average cannot be used for calculating atomic mass.
Important Calculation Notes
All values inputted into this calculator are equally weighted. Please take note of the following when interpreting your results:
- A weighted average should be calculated when some of the values are more important, numerous, frequent, or have a larger sample size than others.
- The geometric mean should only be calculated when it is mathematically possible, which usually means that all values are positive.
- Results might be rounded off to two decimal places.
- At the moment, the tool does not display such calculations as mode, variance, standard deviation, quartiles, and weighted average.
- Ensure that all values are measured in the same units before you perform a calculation.
- It is impossible to calculate the average between raw numbers and percentages unless they measure the same quantity.
- Always double-check important financial, scientific, educational, or medical results using the proper method of calculation.
Frequently Asked Questions
What is an average calculator?
The average calculator is a web-based program that sums up a list of values and then divides their sum by the number of values. The average calculator shows the median, geometric mean, sum, count, min, max, and range of the values provided.
How do I calculate the average for a set of values?
Just add up all the values, find out how many values there are, and divide the sum by the number of values. If your numbers are 4, 8, and 12, you have 24 summed up and 3 as the number of values, which gives us 8 as the arithmetic mean.
Is average the same as mean?
"Average" is normally referred to as "mean" in everyday mathematics. But in statistics, an average can be the median, mode, geometric mean, and so on.
What is the difference between mean and median?
The mean is found by dividing the sum of all values by the number of values. The median is the middle value after arranging the numbers in order.
Can I input decimal numbers in this calculator?
Yes, it is possible to input such decimal numbers as 2.5, 4.75, and 9.125. Some calculated results might be rounded to two decimal places.
Can I use negative numbers here in this calculator?
Yes, in calculating the arithmetic mean, sum, median, minimum, maximum, and range, it is possible to use negative numbers. However, a regular geometric mean of real numbers is usually not calculable with negative numbers in the data set.
Does the order of the numbers matter?
No, re-ordering the same set of numbers will have no impact on the arithmetic mean, median, geometric mean, sum, number of elements, minimum, maximum, and range.
Can I use it to calculate my grade average?
Yes, as long as all grades are weighted equally. When your homework, tests, assignments, or even courses carry different weights or credit hours, you need a weighted grade calculation.
Is this tool for computing the weighted average?
No, this tool treats each inputted value as being of the same importance. The computation of a weighted average needs values and weights.
Can it compute the average percentage?
Yes, but only if the percentages are equally weighted and are similar in meaning. Apply the weighted approach if the percentages have been computed using different sample sizes, points, or category weights.
How can I compute an average using Excel?
Use =AVERAGE(A1:A10), and then change the cell reference to that of your data.
Can I apply it to calculate the stock average?
Only if you buy an equal number of stocks each time. If not, you need to divide the total investment amount with the total number of stocks bought.
Can this tool compute a batting average?
No. It cannot calculate a batting average using percentages from individual games. Batting average is computed using total hits divided by total official at-bats.
Is it a calculator of average, median, and mode?
The calculator finds the arithmetic mean and median but does not show the mode now. The calculator also offers geometric mean, sum, count, minimum, maximum, and range.
What can I use the geometric mean for?
The geometric mean is helpful to find the average when dealing with ratios and rates and other values that multiply.
Why is the geometric mean less than the arithmetic mean?
The geometric mean cannot be greater than the arithmetic mean if the values are positive. Large differences can show large variations of values.
What do the range indicate?
Range is the difference between the highest and lowest values in the set of data. It gives the overall spread of the data but does not give any idea regarding the distribution of other values.
Can I calculate an average of the averages?
Yes, but you need to consider the size of the group too. In case the size of different groups varies, then the mean of each group needs to be multiplied by their respective sizes.
What happens when all the numbers are same?
If all the values are the same then the arithmetic mean, median, geometric mean, minimum and maximum will all be equal to that repeated number. Range will be zero.
Can an outlier affect the result?
Yes, an outlier may affect the calculation of the arithmetic mean. You can compare the mean with other statistics like median, minimum, maximum, and range.
