Average Calculator
The average of 10, 20, and 30 is 20 because their sum is 60 and the list contains 3 values. This average calculator returns arithmetic mean, median, mode, count, sum, minimum, maximum, and range from one numeric list. Paste values separated by commas, spaces, tabs, or new lines. The statistics answer different questions. Mean uses every value, median finds the center after sorting, and mode reports the most frequent value or values. Range shows the distance between the minimum and maximum. Comparing them can reveal when an extreme value pulls the mean away from the middle of the data.
Quick answer
The mean is the sum of all values divided by how many values you entered.
What this tells you
- •The mean is the sum of all values divided by how many values you entered.
- •The median is the middle value once the numbers are sorted in order.
- •The mode is the value that appears most often, and a set can have no mode or several.
- •The range is the largest value minus the smallest value.
- •An even-length list uses the average of its two middle sorted values for the median.
- •If several values tie for the highest frequency above one, the calculator lists every mode in ascending order.
- •Mean and median round to no more than 4 decimal places, while count, sum, minimum, maximum, and range come directly from the numeric values.
How to Use
- 1Type or paste your numbers into the input field.
- 2Separate values with commas, spaces, or new lines.
- 3Click Calculate to see mean, median, mode, count, sum, minimum, maximum, and range.
- 4Keep negative signs and decimal points attached to their values. Do not use thousands commas because every comma starts another item.
- 5Check Count before interpreting the result. Duplicate numbers count as separate observations and affect both frequency and mean.
- 6Compare mean with median when the list contains an unusually high or low value, since that value can move the mean sharply.
How It Works
Formula
mean = sum of values / count. median = middle value of the sorted list (average of the two middle values when the count is even). mode = the value that appears most frequently.The mean adds every number and divides by the count, so it reflects the overall total. The median sorts the values and takes the center, which resists the pull of very high or very low numbers. The mode is the most common value and answers which result repeats most. Range subtracts the smallest value from the largest to show the spread.
Calculation note: values are processed in the order shown above, using the current input units.
Worked Examples
Average of 10, 20, 30
Add the values: 10 + 20 + 30 = 60. Divide by the count of 3 to get a mean of 20. Sorted, the middle value is also 20, so the median is 20. The range is 30 minus 10, which is 20. Every value appears once, so there is no mode.
Average of 4, 8, 8, 15
The sum is 35 and the count is 4, so the mean is 8.75. Sorted as 4, 8, 8, 15, the two middle values are 8 and 8, so the median is 8. The value 8 appears twice, making it the mode.
Even number of values
The sum is 10 and count is 4, so mean is 2.5. The sorted middle pair is 2 and 3, whose average is also 2.5. Each value occurs once, so there is no mode.
Two modes
Both 1 and 2 occur twice, which is the highest frequency. The calculator sorts tied modes and displays them as 1, 2. The range is 3 - 1 = 2.
Negative values
The values sum to -9 and the count is 3, giving mean -3. The middle sorted value is -3. Range is -1 minus -5, which equals 4.
Mean rounded to four places
The exact mean is 5/3, a repeating decimal. The calculator rounds it to 1.6667. Median and mode are both 2.
Mean, Median, Mode, and Range
What each statistic measures and how it is found.
| Term | Definition |
|---|---|
| Mean | The sum of all values divided by the count of values. |
| Median | The middle value of the sorted list, or the average of the two middle values. |
| Mode | The value that appears most often, which may be none or several. |
| Range | The largest value minus the smallest value. |
Choosing the statistic that fits the question
Mean is useful when every observation should contribute to one arithmetic balance point. Add the values, then divide by count. It is sensitive to extremes. In the list 2, 3, 4, and 100, the mean is 27.25 even though three of the four values sit below 5. The arithmetic is correct, but the mean alone gives a poor picture of a typical small value in that list.
Median depends on order rather than total. After sorting, take the middle item for an odd count or average the middle pair for an even count. For 2, 3, 4, and 100, median is 3.5. This makes median less sensitive to the single value 100, though it also uses less information about the size of every observation.
Mode is about repetition. If all values occur once, the tool says No mode. If one value has the largest count, it reports that value. If several values share the highest count and that count is greater than one, it returns all of them in numeric order. Duplicates are observations, so removing them changes mode, count, sum, and usually mean.
Range is a quick spread measure, but it looks only at the two endpoints. The sets 1, 2, 3, 9 and 1, 7, 8, 9 both have range 8 even though their internal patterns differ. Standard deviation, quartiles, and interquartile range provide more detail when spread matters.
The input box splits text at commas and whitespace. A token must convert to a finite JavaScript number. Ordinary signed decimals and scientific notation work, but labels, percent signs, currency symbols, and fractions such as 1/2 do not. A blank list or any invalid token prevents calculation.
Common mistakes
- Confusing the mean with the median. The mean is the arithmetic average, while the median is the middle value after sorting, and the two differ when the data is skewed.
- Forgetting to sort before finding the median. The median is only correct once the numbers are arranged from smallest to largest.
- Expecting a mode when every value is unique. If no number repeats, the set has no mode rather than a mode of zero.
- Removing duplicate values before calculation. Repeated observations belong in the list and are necessary for frequency and weighting.
- Using a comma inside a large number. Enter 1500 rather than 1,500 because the comma is treated as a separator.
- Assuming range describes the full distribution. It uses only minimum and maximum and ignores every value between them.
- Rounding input values before pasting them. Input rounding can change mean, median order, and which values tie as modes.
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