Average Calculator
Find the average (mean) of a list of numbers with the median, mode and range, or a weighted average, the average of groups or of a frequency table, with every step shown.
- Count (n)
- 5
- Sum
- 150
- Median (middle value)
- 30
- Mode (most frequent)
- No mode: every value appears once
- Minimum
- 10
- Maximum
- 50
- Range (max − min)
- 40
Your values on a number line
Step-by-step calculation
Step 1: Add all the values
10 + 20 + 30 + 40 + 50 = 150
Step 2: Count the values
n = 5
Step 3: Divide the sum by the count
150 ÷ 5 = 30
Step 4: Answer
Mean (average) = 30
How the median was found
Step 1: Sort the values from smallest to largest
10, 20, 30, 40, 50
Step 2: Take the middle value
With 5 values (an odd count), the median is value number 3.
Median = 30
To measure how spread out the values are around the average, use the Standard Deviation Calculator; to see how far one value sits from the mean, the Z-Score Calculator. For course grades with category weights, try the Weighted Grade Calculator.
An average summarises a set of numbers with one typical value. This average calculator finds the arithmetic mean of any list of numbers (the sum divided by the count) and shows the sum, count, median, mode, minimum, maximum and range alongside it, with a chart marking the mean and median. It also calculates a weighted average, the overall average of groups of different sizes, and the mean of a frequency table.
Paste or type numbers separated by commas, spaces or new lines. Every result comes with a step-by-step calculation that uses your numbers, and you can choose how many decimal places to display.
Average Formula
The average of a set of numbers, called the arithmetic mean, is their total divided by how many there are:
Mean = (x₁ + x₂ + … + xₙ) ÷ n = Σx ÷ n
- x₁, x₂, … xₙ
- The individual values: the first, second and so on up to the last.
- n
- The number of values.
- Σx
- The sum of all the values (Σ means “add up”).
Weighted average formula
Weighted mean = Σ(w × x) ÷ Σw
- x
- Each value, such as a test score.
- w
- Its weight: how much it counts, such as 20% or 2 credits.
- Σ(w × x)
- Each value multiplied by its weight, all added up.
- Σw
- The total of the weights. When the weights are percentages that add to 100, this is 100.
The same formula gives the overall average of several groups (weights = group sizes) and the mean of a frequency table (weights = frequencies).
How to Calculate an Average
- Add all the values. For 6, 8, 10 and 16: 6 + 8 + 10 + 16 = 40
- Count the values. There are 4.
- Divide the sum by the count: 40 ÷ 4 = 10
The average is 10. It doesn’t have to be one of the values, and it can be a decimal even when every value is a whole number: the average of 1, 2, 3 and 5 is 2.75. Negative numbers are added like any other value, so the average of −5, 0 and 5 is 0.
Types of Averages
In everyday use, “average” means the arithmetic mean. The median and mode are different measures of a typical value (measures of central tendency). They are calculated differently and can give very different answers for the same data.
Arithmetic mean
The sum of the values divided by how many there are. This is what people usually mean by “the average”.
Useful for: Data without extreme values, and totals that matter (average spend, average score).
2, 4, 9 → 15 ÷ 3 = 5
Median
The middle value once the values are sorted (or the mean of the two middle values).
Useful for: Skewed data or outliers, such as incomes, house prices or response times.
2, 4, 9 → 4
Mode
The value that occurs most often. A data set can have one mode, several, or none.
Useful for: Categories and repeated values, such as the most common shoe size or rating.
2, 4, 4, 9 → 4
Weighted average
A mean where some values count more than others, according to their weights.
Useful for: Grades with different weightings, portfolio returns, prices bought in different quantities.
80 (×1), 90 (×3) → 87.5
Mean vs Median: When the Average Misleads
The mean uses every value, so one extreme value can move it a long way. Take 10, 10, 10, 10, 100:
- Mean = (10 + 10 + 10 + 10 + 100) ÷ 5 = 140 ÷ 5 = 28
- Median = 10 (the middle of the sorted values)
- Mode = 10 (it appears four times)
Four of the five values are 10, yet the mean is 28, higher than all of them except the outlier. The median ignores how extreme the largest value is, so it still describes the typical value. This is why incomes and house prices are usually reported as medians. When the mean and median are close, the data is roughly symmetric and the mean is a good summary; the calculator flags results where they are far apart.
How to Calculate a Weighted Average
Use a weighted average when some values should count more than others. Multiply each value by its weight, add the results, and divide by the total weight. With scores of 80 (20%), 90 (30%) and 70 (50%):
(80 × 20 + 90 × 30 + 70 × 50) ÷ (20 + 30 + 50)
= (1,600 + 2,700 + 3,500) ÷ 100 = 7,800 ÷ 100 = 78
The simple mean of 80, 90 and 70 is 80, but the weighted average is 78 because the lowest score carries half the weight. Weights can be percentages or relative weights: 20, 30, 50 and 2, 3, 5 give the same answer because dividing by the total weight rescales them. If percentage weights don’t add up to 100, dividing by their actual total gives the average of the parts entered so far, which is useful when a final exam hasn’t happened yet. For course grades by category, the Weighted Grade Calculator is built for that job.
Average Examples
Exam scores
Scores: 70, 80, 90, 85, 75
Mean = sum ÷ count
70 + 80 + 90 + 85 + 75 = 400
400 ÷ 5 = 80
Average score: 80
Monthly expenses
January 10,000 · February 12,000 · March 9,000 (any currency)
Mean = sum ÷ count
10,000 + 12,000 + 9,000 = 31,000
31,000 ÷ 3 = 10,333.33…
Average monthly spending: about 10,333.33
Product ratings
Ratings: 4, 5, 3, 5, 4 (out of 5)
Mean = sum ÷ count
4 + 5 + 3 + 5 + 4 = 21
21 ÷ 5 = 4.2
Average rating: 4.2 stars (mode 4 and 5, median 4)
Weighted grades
Homework 80 (20%) · Exam 90 (50%) · Project 85 (30%)
Weighted mean = Σ(w × x) ÷ Σw
80 × 20 + 90 × 50 + 85 × 30 = 1,600 + 4,500 + 2,550 = 8,650
Σw = 20 + 50 + 30 = 100
8,650 ÷ 100 = 86.5
Weighted average: 86.5 (a simple mean would give 85)
When Should You Use an Average?
- Use the mean when values are fairly evenly spread and the total matters: average spending, average test score, average daily temperature.
- Use the median when the data is skewed or has outliers: salaries, property prices, delivery times.
- Use the mode for the most common option: the most popular size, the most frequent rating.
- Use a weighted average when items have different importance or sizes: grades with weightings, the combined average of classes of different sizes, an average price paid across several purchases.
An average on its own hides how spread out the data is: 49, 50, 51 and 0, 50, 100 both average 50. Pair it with the range or the standard deviation to describe the spread, and use the Z-Score Calculator to see how unusual a single value is. To compare two quantities rather than summarise many, use the Ratio Calculator; to express a value as a share of a total, the Percentage Calculator.
How to Use the Average Calculator
- Choose a mode: an average of a list of numbers, a weighted average, the overall average of several groups, or the mean of a frequency table.
- Type or paste your numbers separated by commas, spaces or new lines (write 10000 rather than 10,000), or fill in the value and weight rows.
- Pick how many decimal places to display. Calculations always use full precision; only the displayed results are rounded.
- Read the average, the summary statistics and the chart, then follow the step-by-step calculation, which uses your numbers.
- Compare the mean with the median: if they are far apart, a few extreme values are pulling the mean, and the median may describe a typical value better.
Frequently Asked Questions
How do you calculate an average?
Add all the values and divide by how many values there are. For 12, 15, 18 and 25: 12 + 15 + 18 + 25 = 70, and 70 ÷ 4 = 17.5.
What is the formula for average?
Average (mean) = (x₁ + x₂ + … + xₙ) ÷ n, where x₁ to xₙ are the values and n is the number of values. It is often written Σx ÷ n.
What is the difference between mean and average?
In everyday use they mean the same thing: the arithmetic mean, the sum divided by the count. In statistics, “average” can also loosely refer to other measures of a typical value, such as the median or mode.
How do you calculate the average of multiple numbers?
The method is the same however many numbers you have: add them all and divide by the count. The average of 10, 20, 30, 40 and 50 is 150 ÷ 5 = 30. You can paste thousands of values into the calculator at once.
How do you calculate a weighted average?
Multiply each value by its weight, add the products and divide by the sum of the weights. For 80 (20%), 90 (30%) and 70 (50%): (1,600 + 2,700 + 3,500) ÷ 100 = 78.
What is the difference between mean, median and mode?
The mean is the sum divided by the count, the median is the middle value after sorting, and the mode is the value that occurs most often. For 2, 4, 4, 10 the mean is 5, the median is 4 and the mode is 4.
Can an average be a decimal?
Yes. The average of whole numbers is often a decimal: the average of 1, 2, 3 and 5 is 11 ÷ 4 = 2.75. Round it only at the end, to the precision you need.
Can negative numbers be included in an average?
Yes. Negative values are added like any other number, so they pull the average down. The average of −5, 0 and 5 is 0 ÷ 3 = 0.
How does an outlier affect the average?
An outlier can pull the mean strongly towards it. The mean of 10, 10, 10, 10 and 100 is 28 even though four values are 10. The median (10) is barely affected, which is why it is preferred for skewed data.
What is the difference between average and median?
The average (mean) uses the size of every value; the median only depends on the middle position of the sorted values. They are equal for symmetric data, but with a few very large or small values the mean moves towards them while the median does not.
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Last updated: September 29, 2026.