Calculate the average (mean), median, mode, and range of any set of numbers. Enter values separated by spaces or commas for instant results.
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An Average Calculator is a mathematical tool that computes the central tendency of a set of numbers. The most common type of average is the arithmetic mean, which is found by summing all values and dividing by the number of values.
The mathematical formula for calculating the arithmetic mean is:
x̄ = x₁ + x₂ + x₃ + ... + xₙn = Σxn
Where x̄ is the mean, Σx is the sum of all values, and n is the count
This calculator also computes other important statistical measures including median (middle value), mode (most frequent value), and range (difference between max and min), providing a complete picture of your data's central tendency.
The sum of all values divided by the count of values. Most commonly used average.
Mean = Σx ÷ n
Example: (10+20+30) ÷ 3 = 20
The middle value when data is sorted. If even count, average of two middle values.
Sorted: 5, 10, 15, 20, 25
Median = 15 (middle value)
The value that appears most frequently in the dataset. Can have multiple modes.
Data: 5, 10, 10, 15, 10, 20
Mode = 10 (appears 3 times)
The difference between the largest and smallest values in the dataset.
Range = Max - Min
Example: 100 - 20 = 80
Type your numbers in the text box. Separate them with spaces, commas, or new lines. Example: "10 20 30 40" or "10, 20, 30, 40"
The calculator automatically computes and displays the mean, median, mode, range, and other statistics as you type.
Review all computed values including mean, median, mode, range, variance, and standard deviation for comprehensive data analysis.
Given:
Test scores: 85, 90, 78, 92, 88
Solution:
Sum = 85 + 90 + 78 + 92 + 88 = 433
Count = 5
Mean = 433 ÷ 5 = 86.6
Given:
Values: 12, 5, 22, 30, 7, 36, 14
Solution:
Sorted: 5, 7, 12, 14, 22, 30, 36
Middle position = (7+1)/2 = 4th
Median = 14
Given:
Values: 2, 4, 4, 6, 6, 8, 8, 8
Solution:
4 appears 2 times
6 appears 2 times
8 appears 3 times (most frequent)
Mode = 8
Scenario:
Salaries: ₹30,000, ₹35,000, ₹32,000, ₹28,000, ₹5,00,000
Analysis:
Mean = ₹1,25,000 (distorted by outlier)
Median = ₹32,000 (more representative)
Median is better when outliers exist!
Averages can be distorted by extreme values (outliers). A single very high or very low value can significantly shift the mean away from what most data points represent.
Example: Average Income Distortion
Room with 10 people earning ₹50,000 each + 1 billionaire
Mean income = ₹9,09,09,545 (misleading!)
Median income = ₹50,000 (accurate representation)
Tip: Always check for outliers and consider using the median when your data might have extreme values.
Get mean, median, mode, range, variance, and standard deviation all at once.
Results update automatically as you type - no need to click calculate.
Enter numbers separated by spaces, commas, or new lines - whatever works for you.
Handle dozens or hundreds of values with ease.
Shows formulas and step-by-step calculation process.
Free to use, no registration, and your data stays private.
In common usage, "average" and "mean" refer to the same thing - the arithmetic mean. However, technically "average" can refer to any measure of central tendency (mean, median, or mode). When people say "average," they usually mean the arithmetic mean: sum of all values divided by count.
If all percentages represent equal-sized groups, you can simply average them. However, if they represent different-sized groups, you need a weighted average. For example, if Class A (30 students) averaged 80% and Class B (20 students) averaged 90%, the overall average is (30×80 + 20×90)/(30+20) = 84%, not simply (80+90)/2 = 85%.
The mean is affected by every value, including outliers, while the median only looks at the middle position. If your mean and median are very different, it usually indicates your data is skewed or has outliers. Symmetric data will have similar mean and median values.
You can only average averages if each group has the same size. Otherwise, you need the weighted average. For example, averaging exam scores from different sections only works if each section has the same number of students.
When no mode is displayed, it means either all values appear only once (no repetition) or all values appear the same number of times. In either case, there's no single value that's more common than others.
Use the AVERAGE function: =AVERAGE(A1:A10) for cells A1 to A10. For median, use =MEDIAN(A1:A10). For mode, use =MODE(A1:A10) or =MODE.MULT(A1:A10) for multiple modes.
Standard deviation (σ) measures how spread out the data is from the mean. A low standard deviation means values are close to the mean; a high standard deviation means they're spread over a wider range. It's calculated as the square root of variance.
Use median when: (1) Your data has outliers that could skew the mean, (2) The distribution is not symmetric, (3) You're dealing with income, house prices, or any data where extreme values are common, (4) You want the "typical" value that 50% of data falls above and below.
Generally, use one more decimal place than your original data. For whole numbers, one or two decimal places is usually sufficient. For scientific or financial calculations, you may need more precision. Our calculator shows up to 4 decimal places.
No! All calculations happen in your browser. We don't store, track, or transmit any numbers you enter. Your data privacy is completely protected.
Before relying on the mean, scan your data for extreme values that might distort the result.
When presenting data, show both mean and median to give a fuller picture.
An average of 50 means different things for test scores (failing) vs. age (middle-aged).
Average alone doesn't tell the whole story. Include range to show data spread.
Averages from small samples may not be reliable. Larger samples give more stable results.
Only average averages if groups are equal size; otherwise use weighted averages.