Average Calculator
Mean, median, mode, range and standard deviation of a list of numbers, with the list sorted.
Your numbers
Filled in with example values. Replace them with your own.
Paste a column from a spreadsheet if you like. Use a dot for decimals (2.5), not a comma.
Results update as you type.
Result
Mean: 5
Mean (average)
5
- MedianThe middle value when sorted
- 4.5
- ModeAppears 3 times
- 4
- Range9 − 2
- 7
- Smallest · largest
- 2 · 9
- Count · sum
- 8 · 40
- Standard deviationPopulation (÷ n)
- 2
- Standard deviationSample (÷ n − 1)
- 2.138089935
- Geometric meanAll values positive
- 4.603215596
Sorted
2, 4, 4, 4, 5, 5, 7, 9
How it’s calculated
Mean
40 ÷ 8 = 5
Median
(4 + 5) ÷ 2, the two middle values = 4.5
Range
9 − 2 = 7
How the average calculator works
Enter or paste a list of numbers. The calculator sorts them and works out the mean, median and mode, the range, the smallest and largest values, the count and sum, the standard deviation and, when every value is positive, the geometric mean.
The formulas
Mean = Sum ÷ Count
Median = middle value (or mean of the two middle values)
Range = Largest − Smallest
Standard deviation = √(Σ(x − mean)² ÷ n) (sample: ÷ (n − 1))
Worked example
For 2, 4, 4, 4, 5, 5, 7, 9:
- Mean: 40 ÷ 8 = 5
- Median: the two middle values are 4 and 5, so 4.5
- Mode: 4 (three times); range: 9 − 2 = 7
- Standard deviation: 2 as a population, 2.14 as a sample
Frequently asked questions
What is the difference between mean, median and mode?
The mean is the sum divided by the count, the everyday “average”. The median is the middle value once the numbers are sorted. The mode is the value that appears most often. With a few very large or small values, the median is often more representative than the mean.
Which standard deviation should I use?
Use the population version (dividing by n) when your numbers are the whole group you care about. Use the sample version (dividing by n − 1) when they are a sample from a larger group, as in most surveys and experiments.
What if there is no mode?
If every value appears the same number of times, none is more common than the others, so there is no mode. If several values tie for most common, all of them are shown.
What is the geometric mean for?
It averages values that multiply together, such as growth rates. It is only defined here when every value is positive.