Mean, Median & Mode Calculator
Calculate mean, median, mode, range, and variance for a set of numbers. Enter up to 20 values.
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How to use this calculator
Mean is the arithmetic average; median is the middle value when sorted; mode is the value that appears most often.
- 1
Enter your data values in the input fields (up to 8; optional fields are skipped if 0).
- 2
The calculator shows mean, median, mode, range, variance, and standard deviation.
- 3
Use the standard deviation calculator for larger datasets.
Frequently asked questions
Is the variance here the population or the sample variance?
Population variance: the squared distances from the mean are summed and divided by n, not n − 1. For the values 4, 7, 2, 9 and 4 it returns 6.16 and a standard deviation of 2.4819. If your numbers are a sample drawn from a bigger group and you want the sample variance, multiply the variance shown by n ÷ (n − 1).
How many values can I enter, and what happens to the optional fields?
There are eight fields. Values 1 to 5 are always used, including a genuine 0. Values 6 to 8 are skipped when they are 0, because an empty field and a typed 0 look the same to the calculator. That means a dataset that really contains a zero in positions 6 to 8 cannot be entered; put the zero in one of the first five slots instead.
What does “No mode” mean?
It appears when every value occurs exactly once, as with 1, 2, 3, 4, 5. When two or more values tie for the highest count, the calculator lists all of them: 3, 1, 2, 2, 3, 5, 5, 9 returns the modes 2, 3, 5. When all values are identical, such as five 5s, the mode is that single value.
How is the median found with an even number of values?
The values are sorted and the two middle ones are averaged. For 10, 20, 20, 30, 90 and 40 the sorted list is 10, 20, 20, 30, 40, 90, so the median is (20 + 30) ÷ 2 = 25. With an odd count the median is simply the middle value and is always one of your numbers.
Why are the mean and median so far apart in some results?
Because of skew or an outlier. In the set 10, 20, 20, 30, 40, 90 the mean is 35 but the median is 25, since the 90 pulls the average upward while barely moving the middle. A large gap between the two is a hint to look at the extreme values before trusting the mean.
Does the order I enter the numbers matter?
No. The calculator sorts internally for the median and range, and counts frequencies for the mode, so any order gives the same answers.
Can I use negative numbers or decimals?
Yes. Both are accepted, and results are shown rounded to four decimal places with trailing zeros dropped. The range is the largest value minus the smallest, so it is never negative.
Mean, median and mode calculator — averages and spread for up to eight numbers
What each statistic reports
Mean, median and mode answer different questions about the same list. The mean adds the values and divides by the count, so every number influences it. The median is the middle of the sorted list. The mode is the most frequent value. Alongside them, the calculator reports range, population variance, standard deviation and the count used.
| Statistic | How it is found | Result |
|---|---|---|
| Mean | Sum ÷ count | 5.2 |
| Median | Middle of 2, 4, 4, 7, 9 | 4 |
| Mode | Most frequent value | 4 |
| Range | 9 − 2 | 7 |
| Variance | Mean squared deviation (÷ n) | 6.16 |
| Standard deviation | Square root of variance | 2.4819 |
Worked example: an outlier distorts the mean
Take six response times in seconds: 10, 20, 20, 30, 90 and 40. The calculator gives a mean of 35, a median of 25, a mode of 20, a range of 80 and a standard deviation of 26.2996. Five of the six values are 40 or below, yet the mean sits at 35 because of the single 90. The median of 25 describes the typical value better here. Remove the 40 and the mean drops to 34 while the median falls to 20, which shows how a change in one value moves the two measures differently.
Worked example: several modes
For 3, 1, 2, 2, 3, 5, 5, 9 the calculator returns a mean of 3.75, a median of 3 and a variance of 5.6875, and lists three modes: 2, 3 and 5, each appearing twice. A list with ties like this is called multimodal. Reporting a single mode would hide that, so every tied value is shown.
Choosing between the three averages
Use the mean when values are fairly symmetric and you want every observation to count, such as repeated measurements of one quantity. Use the median when a few extreme values would mislead, as with incomes or waiting times. Use the mode for categories or repeated whole-number answers, such as the most common shoe size. Reporting the mean together with the standard deviation tells a reader how tightly the numbers cluster.
Population versus sample
The variance and standard deviation here divide by n, which treats your list as the entire population. If the list is a sample used to estimate a larger group, statisticians divide by n − 1 instead, producing a slightly larger number. Multiply the reported variance by n ÷ (n − 1) to get it, then take the square root for the sample standard deviation.
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