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Average Calculator

Paste any list of numbers and get the mean (average), median, mode, range, sum, count, smallest and largest value, plus the variance and standard deviation for a population and for a sample. A second mode calculates a weighted average, for example a course grade where each mark has a different weight. Mistyped entries are named so you can fix them quickly.

Math Runs in your browser

Find the Average of Your Numbers

Calculated with exact fractions, so the mean of 0.1 and 0.2 is exactly 0.15. Standard deviation is shown for both a whole population (divide by n) and a sample (divide by n − 1).

Separate with commas, spaces or new lines. Use a full stop for decimals, no thousands separators.

How to Use the Average Calculator

  1. Choose a list of numbers or a weighted average.
  2. Type or paste the numbers (or value–weight pairs, one per line).
  3. Pick the decimal places and number format if you need them, and press Calculate.
  4. Read the results; the working lists the sorted values and the formulas.

About This Tool

Students working on statistics homework or grade averages, teachers, analysts checking a data column, and anyone who needs a quick mean and spread.

Input: Numbers  ·  Output: Statistics.

Features and Limitations

Features

  • Mean, median, mode(s), range, sum, count, minimum and maximum.
  • Population and sample variance and standard deviation.
  • Weighted average with a table of value × weight.
  • Names every value that is not a number.
  • Up to 5,000 numbers at once.

Limitations

  • Standard deviations are irrational for most data, so they are rounded and shown with “≈”.
  • Sample standard deviation needs at least two numbers.
  • Percentages, fractions such as 1/2 and thousands separators are not accepted inside the list: convert them to plain decimals first.
  • Weighted average needs at least one weight above zero.
  • Results are computed in your browser; nothing you enter is sent to a server.

Example

For 12, 15, 15, 18, 22, 30: sum 112, count 6, mean 18.6667 (to 4 decimals), median 16.5, mode 15, range 18. For marks 85, 90, 72 with weights 30, 20, 50 the weighted average is (85×30 + 90×20 + 72×50) ÷ 100 = 79.5.

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 of the sorted list (the average of the two middle values if the count is even). The mode is the value that appears most often. Outliers move the mean far more than the median.

When should I use population or sample standard deviation?

Use the population version (divide by n) when your numbers are the whole group you care about. Use the sample version (divide by n − 1) when they are a sample from a larger group; it corrects the tendency of a sample to underestimate spread.

How is a weighted average calculated?

Weighted average = Σ(value × weight) ÷ Σ(weight). A heavier weight pulls the result towards that value, so a 50-credit course counts more than a 20-credit course.

What if there is more than one mode, or none?

If several values tie for the highest frequency, all of them are listed. If every value occurs once, the list has no mode and the page says so.

Which values does the tool reject?

Anything that is not a plain number, such as “abc”, “1,5”, “12%” or “1/2”. The error message names each bad entry so you can correct it.

Related Tools

More like this: all Math tools, all Calculators tools or the TinySandy home page.