Average Calculator - Mean, Median, Mode, Range

Paste a list of numbers and instantly get the mean, median, mode, range, sum, and geometric and harmonic means. Free and browser-based: your data never leaves your device.

Results

Mean (average)

15

Count6
Sum90
Mean (average)15
Median15
Mode15
Minimum9
Maximum21
Range12
Geometric mean14.4716
Harmonic mean13.9227

Mean, Median, Mode, and When Each One Matters

The mean is what most people call "the average": add everything up and divide by the count. For the list 12, 15, 9, 21, 15, 18 the sum is 90 and the mean is 15. The median is the middle value once the list is sorted (or the midpoint of the two middle values for an even count), and the mode is the value that appears most often. Each answers a different question, and picking the wrong one is a classic way to mislead with statistics.

The mean is sensitive to outliers, the median is not. In a room of nine people earning 3,000 per month and one earning 100,000, the mean income is 12,700 while the median stays at 3,000, which describes the room far better. That is why house prices and incomes are almost always reported as medians. The mode is most useful for categorical or repeated data, like the most common shoe size sold or the most frequent score in a class. A list where every value occurs once has no mode at all.

The geometric mean multiplies the n values and takes the nth root, and is the right average for growth rates and returns. An investment that gains 50% one year and loses 50% the next has an arithmetic mean return of 0%, but the geometric mean of the growth factors (1.5 and 0.5) is about 0.866, correctly showing you lost roughly 13.4% per year on average. The harmonic mean (n divided by the sum of reciprocals) is correct for averaging rates: drive the same route at 60 km/h out and 40 km/h back and your true average speed is the harmonic mean, 48 km/h, not 50. Both require strictly positive numbers, and for any dataset the harmonic mean is never above the geometric mean, which is never above the arithmetic mean.

This calculator accepts numbers separated by commas, spaces, semicolons, or new lines, so you can paste a column straight from a spreadsheet. Invalid entries are skipped and reported rather than silently breaking the result, and the copy button exports all statistics as plain text. For related math, ToolForte's Percentage Calculator handles percent changes and the Grade Calculator turns scores into weighted course grades. Everything runs free in your browser.

How the Average Calculator Works

  1. 01Paste or type your numbers, separated by commas, spaces, or new lines.
  2. 02The statistics update live: mean, median, mode, range, min, max, sum, and count.
  3. 03Geometric and harmonic means appear when all values are positive.
  4. 04Click Copy Results to export everything as plain text.

Mean, Median, and Mode in Practice

The mean is the sum divided by the count; the median is the middle value of the sorted list; the mode is the most frequent value. They can differ sharply: one large outlier drags the mean while leaving the median untouched, which is why incomes and house prices are reported as medians. The calculator also computes the geometric mean (correct for growth rates) and harmonic mean (correct for averaging rates like speeds), both defined only for strictly positive numbers.

When to Use This Tool

Use it for grading and test scores, sports statistics, sales figures, survey responses, lab measurements, or any pasted spreadsheet column you want summarized instantly without formulas. Because invalid entries are skipped and reported, you can paste messy data with headers or stray text and still get correct statistics on the numeric part.

Common Use Cases

Tips

  • Paste directly from a spreadsheet column; new lines work as separators.
  • Report medians for skewed data like incomes; outliers distort the mean.
  • Harmonic mean is never higher than geometric, which is never higher than arithmetic; use that as a sanity check.

Frequently Asked Questions

What is the difference between mean and median?→
The mean adds all values and divides by the count; the median is the middle of the sorted list. For 1, 2, 3, 4, 100 the mean is 22 but the median is 3. When data has outliers or is skewed, the median usually describes the typical value better.
What if there is no mode?→
If every value appears exactly once, the dataset has no mode and the calculator says so. If two or more values tie for the highest frequency, all of them are listed: 1, 2, 2, 3, 3 is bimodal with modes 2 and 3.
When should I use the geometric mean?→
For growth rates, investment returns, and anything multiplicative. Gaining 50% then losing 50% averages to 0% arithmetically, but the geometric mean of the growth factors 1.5 and 0.5 is about 0.866, correctly showing a 13.4% average annual loss.
When is the harmonic mean the right average?→
When averaging rates over a fixed quantity, like speeds over the same distance. Driving a route at 60 km/h out and 40 km/h back averages 48 km/h (the harmonic mean), not 50, because you spend more time at the slower speed.
What formats can I paste?→
Numbers separated by commas, spaces, semicolons, or new lines, including a column copied straight from Excel or Google Sheets. Decimals with a point work directly; entries that are not numbers are skipped and listed so nothing silently distorts the result.

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