Average Calculator
Calculate arithmetic and weighted averages, median, mode, sum, count and range instantly. Free online statistics calculator with optional weights.
Statistical summary
- Arithmetic mean
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- Median
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- Mode
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- Total sum
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- Count of numbers
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- Minimum
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- Maximum
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- Range
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Results display up to 10 significant digits. Calculations use standard floating-point precision; no rounding is applied to inputs.
How to Calculate Averages: Mean, Weighted Mean, Median and Mode
An average summarizes a set of observations, but the right measure depends on the question. Use the arithmetic mean for equal contributions, a weighted mean for unequal importance, and the median or mode to describe the center without relying on the sum alone. This free average calculator processes your numbers locally in your browser.
Average formulas and summary statistics
- Arithmetic mean Mean = Σx ÷ n. Add every observation and divide by the number of observations, including repeated values and zeros. All values must use comparable units.
- Weighted mean Weighted mean = Σ(x × w) ÷ Σw. Each value has one nonnegative weight; at least one weight must be positive. Weights can represent frequencies, credits or proportions and need not total 100. A zero weight excludes a value only from the weighted mean.
- Median Sort the values from smallest to largest. For an odd count, select the middle observation; for an even count, average the two middle observations.
- Mode The mode is the most frequent value. Multiple values may tie for the highest frequency. This calculator reports no mode when every value appears only once; decimal values must match exactly to count as repeats.
- Sum, count and range Sum = Σx; count = n; range = maximum − minimum. Minimum and maximum identify the endpoints. These unweighted summaries include every entered value.
- Precision Inputs are not rounded. Displayed answers use up to 10 significant digits and the browser’s floating-point arithmetic, so tiny rounding differences are possible. Keep extra precision until the final reporting step.
Step-by-step examples
- Arithmetic average: 4, 6, 8 Add 4 + 6 + 8 = 18. Count the three values. Divide 18 ÷ 3 = 6. The median is also 6, and there is no mode.
- Weighted grades: 80 and 90 Assign weights 1 and 3. Multiply: 80 × 1 = 80 and 90 × 3 = 270. Add the products to get 350 and the weights to get 4. Divide 350 ÷ 4 = 87.5. The ordinary mean is 85.
- Median and mode: 2, 2, 3, 9 The sorted list is already in order. The middle pair is 2 and 3, so the median is 2.5. The mode is 2 because it occurs twice. Sum = 16, count = 4, mean = 4, range = 7.
Mean vs. median vs. mode
- Choosing a measure The mean uses all values and is sensitive to outliers. For 10, 10, 100, the mean is 40 but the median and mode are 10. The median often better represents a typical observation in skewed data.
- Combining groups Do not simply average group averages when group sizes differ. Weight each group mean by its count. For rates or percentages, check denominators and compatible units before combining them.
Average Calculator FAQ
How do I calculate an average of numbers?
Add the numbers and divide by how many there are. For 5, 10 and 15, the sum is 30 and the count is 3, so the average is 10.
What is the difference between arithmetic and weighted mean?
An arithmetic mean gives each number equal influence. A weighted mean multiplies each number by its assigned weight before dividing by the total weight. Equal positive weights produce the ordinary mean.
Can I calculate averages of negative numbers and decimals?
Yes. Negative values, zeros, decimals and scientific notation are supported. Use a decimal point and separate values with commas, spaces or line breaks; a comma always separates numbers.
Do weights have to add up to 100?
No. Weights 1 and 3 give the same result as 25 and 75. Only their relative size matters, provided all are nonnegative and their sum is positive.
Can a dataset have more than one mode?
Yes. If 1 and 2 each occur twice and 3 occurs once, both 1 and 2 are modes. If all values occur once, this calculator shows no mode.
Are median and mode weighted when I enter weights?
No. Optional weights affect only the weighted mean. Mean, median, mode, sum, count and range always describe the original unweighted number list.
Why is my average different from the median?
The mean responds to every value, including extreme observations. The median depends on sorted positions, so the two often differ when the distribution is skewed.
Are my numbers saved or sent to a server?
The calculator’s number inputs and calculations stay in your browser; they are not stored or sent by this tool. This does not describe separate site analytics or advertising.