Average Calculator
Mean, median, and range for any list of numbers with steps shown.
What it does
An average usually means the arithmetic mean: add every value and divide by how many there are. It answers the share each item would hold if the total were split evenly, which is why grades, speeds, and budgets lean on it.
The tool above takes a plain list typed with commas or spaces. It returns the mean, the median middle value, and the range from smallest to largest, with a mode check in the note naming repeats or the lack of them.
Mean and median differ in what they follow. The mean follows every value, so one large outlier drags it upward, while the median follows order alone and stays put. Income and house price reports show medians for exactly this reason.
Definitions here follow standard statistics references such as the NIST handbook and school probability units from Khan Academy. The same formulas grade homework sets, lab repeats, and sports splits without change.
How to use
- Type the numbers with commas, spaces, or line style mixes of both.
- Include 2 to 200 plain numbers. Percent signs and units stay out.
- Read the mean first for the even share value.
- Read the median to see the middle order position.
- Use the range plus the mode note to judge spread and repeats.
Formula
- sum
- Total of all entered values.
- count
- How many values were entered.
- median
- Middle order value after sorting.
- range
- Largest minus smallest value.
Mode names the most frequent value when one repeats clearly. With all unique values there is no mode, and with several values tied the note says so instead of picking blindly.
Worked example
Example: 4, 8, 15, 16, 23, 42
Six values entered with commas.
- Count: 6 values. Sum: 4 + 8 + 15 + 16 + 23 + 42 = 108.
- Mean: 108 / 6 = 18.
- Sort: 4, 8, 15, 16, 23, 42. Two middles are 15 and 16.
- Median: (15 + 16) / 2 = 15.5. Range: 42 - 4 = 38.
- Mode check: every value appears once, so no repeat. Tool shows 18, 15.5, 38.
Reference table
| Measure | Value here | What it tells |
|---|---|---|
| Mean | 18 | Even share across all six |
| Median | 15.5 | Middle order, outlier resistant |
| Range | 38 | Full span from 4 to 42 |
| Mode | no repeat | Nothing repeats here |
Limits
- Mean drifts with outliers. One huge value can dominate small lists.
- Numbers only. Labels, percents with signs, and blanks are rejected.
- Lists cap at 200 values to keep the page instant.
- Weighted or trimmed averages need their own weights and rules.
Common mistakes
- Dividing by the wrong count after skipping a value.
- Reading the median from unsorted order.
- Averaging averages from different sized groups without weighting.
- Rounding each value before adding instead of once at the end.
- Calling the highest count a mode when several values tie.
Try it yourself
Quick checks. Answers sit tucked under each question.
Mean of 10, 20, 30?
Sum 60 / 3 = 20.
Median of 3, 1, 2?
Sorted 1, 2, 3. Middle is 2.
Range of 5, 9, 14?
14 - 5 = 9.
Questions
How do you calculate the average?
Add every value and divide by the count. For 4, 8, 15, 16, 23, 42 the sum is 108 and the mean is 18.
Mean vs median?
Mean splits the total evenly, median takes the middle order slot. Skew and outliers move the mean more.
What is the mode?
The most frequent value. This page checks it in the note: no repeat, one mode, or several tied.
What is the range?
Max minus min. Here 42 minus 4 is 38.
Can I paste decimals and negatives?
Yes. Dots, minus signs, and scientific e notation all parse; letters do not.
Why is the median safer for incomes?
A few very high earners lift the mean far above typical pay, while the median stays at the middle earner.