Mean, Median, Mode Calculator
This calculator finds the mean, median, mode and range of any list of numbers and shows the working for each one. Paste or type your values in any order; it sorts them, builds a frequency table and plots the sorted values on a dot chart. For the default list 3, 7, 7, 2, 9, 4, 7, 5, the mean is 5.5, the median 6, the mode 7 and the range 7.
How to use the mean, median, mode calculator
- Type or paste your numbers into the box, separated by commas or spaces. The default list is
3, 7, 7, 2, 9, 4, 7, 5. - The calculator sorts the list and shows it, so you can check every value was read correctly.
- Read the four results: mean 5.5, median 6, mode 7 and range 7 for the default list.
- Open the worked panel for any measure to see each step, and use the frequency table to see how often each value appears.
The dot chart plots the sorted values in order, so clusters and gaps are easy to see — in the default list, the three 7s sit together just above the middle. When no value repeats, the calculator says there is no mode; when two or more values tie for most frequent, it lists all of them.
Mean, median, mode and range: the four formulas
Each measure answers a different question about the same list. The default data shows all four side by side.
Mean
The mean is the value every item would have if the total were shared out evenly. It uses every number, which makes it sensitive to extreme values.
Median
The median is the middle of the sorted list. With an even count it is the average of the middle two, so it does not have to be one of your numbers. The guide to finding the median covers odd and even lists, frequency tables and grouped data in detail.
Mode
The mode is the only one of the four that works for categories as well as numbers — the most common shoe size or the most popular answer to a survey. The guide to finding the mode deals with ties and lists with no mode.
Range
The range tells you how far apart the extremes are. It is quick to find but depends on only two values. More on its uses and pitfalls is in how to find the range.
Worked examples
Example: seven test scores
Scores of 82, 91, 76, 91, 68, 88 and 95.
The median is higher than the mean because one low score, the 68, pulls the mean down. The mode is the top of the class, which says little about a typical student; with small lists the mode is often not a useful summary. To turn a raw test score into a percentage and letter first, use the grade calculator.
Example: a list with no mode
The values 4, 9, 1, 6.
When every value appears the same number of times, there is no mode. Some textbooks say “every value is a mode”; the more common convention, and the one the calculator uses, is to report no mode.
Example: two modes
The values 2, 3, 3, 5, 8, 8, 10.
A list with two modes is called bimodal. Both are reported; do not average them into a single mode of 5.5.
Example: negatives and decimals
The values −4, −1, 0, 2, 2, 6.
Subtracting a negative minimum adds to the range, which is the rule covered in negative number rules. Decimals need no special handling: 1.5, 2.25, 2.25, 3, 4.5 has mean 2.7, median 2.25, mode 2.25 and range 3.
What one extra value does to each measure
A useful way to understand the four measures is to add one number to the default list and watch which results move.
| List | Mean | Median | Mode | Range |
|---|---|---|---|---|
| Default (8 values) | 5.5 | 6 | 7 | 7 |
| Add 6 | ≈ 5.56 | 6 | 7 | 7 |
| Add 1 | 5 | 5 | 7 | 8 |
| Add 50 | ≈ 10.44 | 7 | 7 | 48 |
Adding 50 nearly doubles the mean and multiplies the range by almost seven, while the median moves by one and the mode does not move at all. That is the core trade-off:
- The mean uses every value’s size, so it is the right summary when totals matter, and the wrong one when a single extreme value is present.
- The median uses only the order, so one huge value can shift it by at most one position.
- The mode only counts repeats, so it ignores size completely.
- The range uses only the two extremes, so an outlier dominates it.
When the mean and median are far apart, the data is skewed, and the median is usually the better summary of a typical value. The guide to finding the average goes further into choosing between them. If you only need the middle value with quartiles and the IQR, the median calculator is built for that.
Reading the frequency table
The frequency table lists each distinct value once, with how many times it occurs. For the default list:
| Value | Frequency | Value × frequency |
|---|---|---|
| 2 | 1 | 2 |
| 3 | 1 | 3 |
| 4 | 1 | 4 |
| 5 | 1 | 5 |
| 7 | 3 | 21 |
| 9 | 1 | 9 |
| Total | 8 | 44 |
All four measures can be read from it. The mode is the row with the highest frequency. The total of the frequency column is n, and the total of the last column is the sum, so the mean is 44 ÷ 8 = 5.5. Counting down the frequencies to positions 4 and 5 gives the median, and the first and last rows give the range. If your data already comes as values with counts, the weighted average calculator takes it in that form directly.
Common mistakes
- Finding the median of an unsorted list. The middle pair of 3, 7, 7, 2, 9, 4, 7, 5 as typed is 2 and 9, giving 5.5; the real median is 6.
- Dividing by the wrong count. Count every value, including repeats and zeros. Dropping the three 7s to one changes both the mean and the median.
- Removing duplicates before finding the mode. The duplicates are the mode.
- Averaging two modes. A bimodal list has two modes, not one in between.
- Reporting the range as “2 to 9.” That is the span; the range is the single number 9 − 2 = 7.
- Rounding before the last step. Keep full precision in the sum and round the mean only at the end, with the rounding calculator if needed.
Frequently asked questions
How do you find the mean, median, mode and range?
Sort the list first. The mean is the sum divided by the count, the median is the middle value (or the average of the middle two), the mode is the most frequent value and the range is the largest minus the smallest. For 3, 7, 7, 2, 9, 4, 7, 5 they are 5.5, 6, 7 and 7.
What is the mean, median and mode of 2, 3, 3, 5, 8, 8 and 10?
The mean is 39 ÷ 7 ≈ 5.57, the median is the 4th value, 5, and there are two modes, 3 and 8, because each appears twice. The range is 10 − 2 = 8. A list with two modes is called bimodal, and both values are reported.
What if there is no mode?
If every value appears the same number of times, the list has no mode. For 4, 9, 1, 6, each number appears once, so there is no mode, while the mean and median are both 5 and the range is 8. The calculator reports “no mode” in this case rather than listing every value.
Can there be more than one mode?
Yes. If two or more values tie for the highest frequency, each is a mode. Two modes make the data bimodal and three or more make it multimodal. In 1, 1, 4, 4, 9 both 1 and 4 appear twice, so both are modes. Do not average them into a single value.
What is the difference between mean and median?
The mean adds every value and divides by the count, so large or small extremes pull it. The median is the middle of the sorted list and only depends on order. Add 50 to the default list and the mean jumps from 5.5 to about 10.44 while the median moves from 6 to 7.
Is the range a measure of the average?
No. The mean, median and mode describe the center of the data, while the range describes its spread: how far apart the smallest and largest values are. It is usually taught alongside them as “mean, median, mode and range” because all four come from the same sorted list.
Can the mean, median and mode be negative or decimals?
Yes. For −4, −1, 0, 2, 2, 6 the mean is about 0.83, the median is 1 and the mode is 2. The range is 6 − (−4) = 10, and it can never be negative because it is the largest value minus the smallest.
Related calculators
Guides that use this calculator
Longer explanations of the method behind it, with worked examples.
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