How to use
- Average & stats: paste numbers separated by commas, spaces or new lines. The mean, median, standard deviation and more appear instantly. A copied spreadsheet column works too.
- Weighted average: put one “value, weight” pair per line — for a GPA, “grade points, credits”.
- Anything that is not a number is skipped, and the tool tells you how many items were ignored. If your data uses thousands separators like 1,234, tick Read commas as thousands separators.
What each statistic means
Using the sample data 70, 85, 90, 65, 85, 80, 95, 70 (8 values):
| Statistic | How it is calculated | Result |
|---|---|---|
| Mean | sum ÷ count | 640 ÷ 8 = 80 |
| Median | the middle value when sorted (average of the two middle values for an even count) | (80 + 85) ÷ 2 = 82.5 |
| Mode | the most frequent value; none if every value appears once | 70, 85 (twice each) |
| Range | maximum − minimum | 95 − 65 = 30 |
| Population variance σ² | sum of squared deviations ÷ n | 800 ÷ 8 = 100 |
| Sample variance s² | sum of squared deviations ÷ (n − 1) | 800 ÷ 7 = 114.29 |
| Standard deviation | square root of the variance | σ = 10, s = 10.69 |
Population vs sample standard deviation
Use the population figure (divide by n) when your data is the whole group — every student in the class. Use the sample figure (divide by n − 1) when your data is a sample used to estimate a larger group, such as 100 survey responses standing in for all customers. In Excel and Google Sheets these are STDEV.P and STDEV.S, and VAR.P and VAR.S for variance.
Weighted average (GPA)
Weighted average = Σ(value × weight) ÷ Σweight
| Course | Grade points | Credits |
|---|---|---|
| Biology | 4.0 | 4 |
| History | 3.7 | 3 |
| Art | 3.0 | 2 |
| Seminar | 2.0 | 1 |
(4.0×4 + 3.7×3 + 3.0×2 + 2.0×1) ÷ 10 = 35.1 ÷ 10 = 3.51. The simple mean of the four grades is 3.175; the weighted figure is higher because the four-credit course counts for more. Grade-point scales and how pass/fail courses count vary by school, so check your institution’s rules.
Things to watch
- The mean is pulled by outliers. Salaries of 42k, 45k, 48k, 51k and 300k average 97.2k, but the median is 48k. For skewed data, look at the median too.
- With a single value, the sample variance and sample standard deviation are undefined and shown as “—”.
- For the change between two averages, use the percent change calculator; to compare parts of a whole, try the ratio calculator.
FAQ
Does this match Excel’s AVERAGE?
Yes. The mean matches AVERAGE, the median matches MEDIAN and the modes match MODE.MULT. The weighted average equals =SUMPRODUCT(values, weights)/SUM(weights).
Why are there several modes?
If two or more values share the highest count, they are all modes. If every value appears only once, there is no mode.