Mean Calculator
Enter a list of numbers to get the arithmetic mean, median and mode, plus the sum, count, minimum, maximum, range and the values in sorted order.
Use a point for decimals, e.g. 1.5. A comma always separates values, so type 1000 rather than 1,000.
Result
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Note: These calculations are for informational purposes only and do not replace professional tax or financial advice. All information without guarantee.
FAQ
Frequently Asked Questions
What is the difference between mean, median, and mode?
The mean is the sum divided by the count. The median is the middle value when sorted. The mode is the most frequent value. Each measures central tendency differently.
When should I use the median instead of the mean?
Use the median when data contains outliers or is skewed (e.g., income data). The median is more robust as it is not affected by extreme values.
How does the calculator determine the median and the mode?
For the median the calculator sorts the values: with an odd count it is the middle value, with an even count the average of the two middle values. Only a value that occurs at least twice counts as the mode – if several values share the highest frequency, all of them are shown; if every value occurs only once, the calculator displays “Kein Modus” (no mode). Example: for 2, 3, 3, 5, 5, 7 the mean is 4.17, the median is (3 + 5) / 2 = 4, and the modes are 3 and 5.
Guide
What is the Mean Calculator?
The mean calculator computes the arithmetic mean, median, mode, sum, minimum, maximum and range of a data set.
How does the Mean Calculator work?
Enter a series of numbers. The calculator computes the arithmetic mean (sum / count), the median (middle value of the sorted series), the mode (most frequent value), the sum, minimum, maximum and range. It does not calculate a weighted mean.
Key Data and Facts
Arithmetic mean = sum of all values / count. Median: middle value of sorted series. Mode: most frequent value. Weighted mean accounts for different weightings.
Step-by-Step Guide
How to calculate averages step by step: 1. Enter the series of numbers: Separate the values with a comma, a semicolon, a space or a line break, and use a point for decimals (1.5, 2.5, 3). Because the comma always separates values, do not use thousands separators. 2. Arithmetic mean: The sum of all values divided by the number of values. Formula: x = (x1 + x2 + ... + xn) / n. 3. Calculate the median: Sort the values. With an odd number: the middle value. With an even number: the average of the two middle values. The median is more robust against outliers than the mean. 4. Determine the mode: The value that occurs most frequently. There can be no mode, one mode or several modes. 5. Weighted mean: Each value is multiplied by a weight and then divided by the sum of the weights. Example: school grades with different ECTS weightings. 6. When to use which average? Arithmetic: the standard case. Median: with outliers (e.g. income distribution). Mode: with categorical data.
Calculation Example
Data set: 3, 5, 7, 7, 9, 15. Arithmetic mean: (3+5+7+7+9+15) / 6 = 7.67. Median: (7+7) / 2 = 7. Mode: 7 (occurs 2x).
Sources
Official sources
Calculations are based on applicable German laws and official data:
Full methodology at Methodology.
Reviewed by Konstantin Iakovlev · Last updated:
Mathematics
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