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Arithmetic Mean
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Enter numbers to calculate
Geometric Mean
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Harmonic Mean
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Weighted Mean
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Median
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Sum
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Min / Max
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Count
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#ValueDev from MeanRank

Calculate the arithmetic mean plus geometric mean, harmonic mean, weighted mean, median, and other summary statistics from any list of numbers.

How It Works

How Average Calculator Works

The arithmetic mean is the sum of all values divided by how many there are. The median is the middle value once the numbers are sorted — or the average of the two middle values when there's an even count.

The geometric mean (the nth root of the product of all values) and harmonic mean (n divided by the sum of each value's reciprocal) are both computed only when every entered number is positive, since taking roots or reciprocals of negative or zero values isn't mathematically valid here. The weighted mean requires a matching list of weights and computes Σ(value × weight) ÷ Σ(weights).

The results table also ranks every entered value from largest (rank 1) to smallest, and shows how far each one deviates from the arithmetic mean — useful for spotting outliers at a glance.

Worked Example

See It In Action

For the numbers 10, 20, 30, 40, 50: the sum is 150 and the arithmetic mean is 30, which also happens to be the median here. The geometric mean is (10×20×30×40×50)^(1/5) ≈ 26.05, and the harmonic mean (5 ÷ (1/10+1/20+1/30+1/40+1/50)) ≈ 21.90 — both lower than the arithmetic mean, since geometric and harmonic means are always pulled down by smaller values in the set.
Real-World Use Cases

Who Uses Average Calculator and Why

  • Comparing arithmetic, geometric, and harmonic means on the same dataset to see which best represents a set of investment returns or rates.
  • Computing a weighted average, like a final grade where different assignments count for different percentages.
  • Using the median instead of the arithmetic mean when a dataset contains outliers that would otherwise skew a simple average.
  • Spotting outliers at a glance using the per-value rank and deviation-from-mean columns in the results table.
Common Mistakes

Mistakes to Avoid

  • Using the arithmetic mean for values that grow multiplicatively over time, like investment returns — the geometric mean correctly accounts for compounding, while the arithmetic mean overstates it.
  • Entering negative or zero values and expecting a geometric or harmonic mean — both require every value to be positive, since they involve roots or reciprocals that break down otherwise.
  • Supplying a weights list that doesn't match the count of values for a weighted mean, which prevents the Σ(value × weight) ÷ Σ(weights) calculation from lining up correctly.
Pro Tips

Tips for Best Results

  • Reach for the geometric mean specifically for growth rates or investment returns, where compounding effects matter.
  • Check the deviation-from-mean column first when you suspect a single unusual value might be distorting your arithmetic mean.
Troubleshooting

Fixing Common Problems

Geometric and harmonic mean aren't showing up in my results. — Both require every entered number to be strictly positive — check your list for any zero or negative values, which make those two means mathematically undefined here.

The weighted mean isn't calculating. — Make sure you've entered exactly one weight per value, in the same order as your numbers list.

Glossary

Terms Explained

Geometric mean: The nth root of the product of all values, best suited to multiplicative data like growth rates.

Weighted mean: An average where each value is scaled by an assigned weight before combining, giving some values more influence than others.

FAQ

Frequently Asked Questions

When should I use geometric mean instead of arithmetic mean?
Geometric mean is the right choice for values that grow multiplicatively over time, like investment returns or growth rates, since it correctly accounts for compounding rather than simply averaging the percentages.
Why don't geometric and harmonic mean show up for negative numbers?
Geometric mean involves taking a root of the product of all values, and harmonic mean involves reciprocals — both break down mathematically (or become undefined/meaningless) if any value is zero or negative, so the calculator only computes them when every number is positive.
What is a weighted average and when do I need one?
A weighted average gives some values more influence than others — for example, averaging test scores where each counts for a different percentage of your grade. You supply one weight per number, and the calculator scales each value by its weight before averaging.
How is the median calculated when there's an even number of values?
The values are sorted, and the median is the average of the two numbers sitting in the middle of that sorted list, rather than a single middle value.