Average Calculator
Paste your numbers to get the mean (average), median, mode, range, standard deviation and more, with the sum-divided-by-count arithmetic shown.
Paste or type numbers separated by commas, spaces or new lines. Decimals and negatives are fine.
- Median
- 88
- Mode
- 92
- Range (max − min)
- 25
- Sum
- 600
- Count
- 7
- Minimum
- 70
- Maximum
- 95
- Geometric mean
- 85.293
- Standard deviation (sample)
- 8.9203
- Standard deviation (population)
- 8.2586
- Variance (sample)
- 79.5714
- Variance (population)
- 68.2041
Sorted from smallest to largest. Highlighted = middle value (median); underlined = mode.
How the mean was calculated
- Add up all 7 numbers: 85 + 92 + 78 + 92 + 88 + 70 + 95 = 600.
- Divide the sum by how many numbers there are: 600 ÷ 7 = 85.714286.
How the median was found
- Sort the numbers from smallest to largest: 70, 78, 85, 88, 92, 92, 95.
- There are 7 numbers (odd), so the median is the middle one, the 4th value: 88.
How the mode was found
- Count how often each value appears.
- 92 appears 2 times, more than any other value, so it is the mode.
How the variance and standard deviation were calculated
- Find the mean: 85.714286.
- Subtract the mean from each value and square the result, then add those squares: Σ(x − mean)² = 477.428571.
- Population variance σ² = 477.428571 ÷ 7 = 68.204082; population standard deviation σ = √68.204082 = 8.258576.
- Sample variance s² = 477.428571 ÷ (7 − 1) = 79.571429; sample standard deviation s = √79.571429 = 8.920282.
How this average calculator works
When people say "average" they almost always mean the arithmetic mean: add up every number, then divide by how many numbers there are. This average calculator does exactly that as you type, and because the same list of numbers is already in hand, it also reports the median, mode, range, geometric mean and standard deviation, so you can see the whole picture of your data instead of a single number.
Paste straight from a spreadsheet column, a text message or a gradebook; commas, spaces and new lines all work as separators, and negative numbers and decimals are fine.
Worked example: averaging test scores
Say a student scored 85, 92, 78, 92, 88, 70 and 95 on seven quizzes. The sum is 600 and there are 7 scores, so the mean is 600 ÷ 7 = 85.71. Sorted, the scores are 70, 78, 85, 88, 92, 92, 95; the middle (4th) value is 88, so the median is 88. The score 92 appears twice while everything else appears once, so the mode is 92. The range is 95 − 70 = 25.
Why are the mean and median different? The one low score of 70 pulls the mean down, while the median just counts positions and ignores how far away the 70 is. That gap is a useful warning sign: when mean and median disagree a lot, a few unusual values are doing the pulling.
Mean vs. median vs. mode: which one to use
Use the mean when every value matters equally and there are no wild outliers: grades, lap times, monthly expenses. Use the median for things like house prices or salaries, where one enormous value would make the mean describe nobody. Use the mode for categories and counts, like the most common shoe size sold. The mean, median, mode calculator puts all three side by side with the middle of the sorted list highlighted.
The geometric mean is the one to use for growth rates. If an investment grows 50% one year and loses 50% the next, the arithmetic mean says 0% per year, but you actually lost 25% overall; the geometric mean of 1.5 and 0.5 is 0.866, a loss of about 13.4% per year, which is the honest answer. The compound interest calculator is built on that idea.
Standard deviation, briefly
Standard deviation measures how spread out the numbers are around the mean. For the quiz scores above the sample standard deviation is about 8.9 points, meaning a typical score sits within roughly 9 points of the average. The calculator shows both the sample version (divide by n − 1, for when your data is a sample from a bigger group) and the population version (divide by n, for when the list is everything). With a handful of values the two differ noticeably; with hundreds they are nearly identical.
Common mistakes
- Averaging averages. If one class of 30 students averaged 80 and another class of 10 averaged 90, the combined average is not 85. Weight by class size: (30 × 80 + 10 × 90) ÷ 40 = 82.5.
- Forgetting zeros. A missing assignment is often a 0, not a blank. Leaving it out of the list raises the average incorrectly.
- Using the mean for weighted grades. If homework is 20% and tests are 80% of a grade, a plain average is wrong; use the grade calculator instead.
Frequently asked questions
›How do you calculate an average?
Add up all the numbers and divide by how many numbers there are. The average of 85, 92, 78, 92, 88, 70 and 95 is 600 ÷ 7 = 85.71.
›What is the difference between mean, median and mode?
The mean is the sum divided by the count. The median is the middle value once the numbers are sorted. The mode is the value that appears most often. For 70, 78, 85, 88, 92, 92, 95 they are 85.71, 88 and 92.
›When is the median better than the mean?
When a few extreme values would drag the mean. Five house prices of $200k, $210k, $220k, $230k and $2M have a mean of $572k but a median of $220k, which better describes a typical house.
›What is the geometric mean?
The nth root of the product of n numbers. It is the right average for growth rates and ratios: the geometric mean of 2 and 8 is √16 = 4, while the ordinary mean is 5. It is only defined when every value is positive.
›Should I use sample or population standard deviation?
Population (divide by n) when your list is the entire group you care about, like every test score in your class. Sample (divide by n − 1) when the list is a sample drawn from a larger group you want to estimate.
›Can I average percentages or grades with this?
Yes, as long as every value carries the same weight. For grades where categories have different weights, use the grade calculator instead.