Mean, Median, Mode and Range Calculator
- Updated
- Formula shown
- Free, no sign-up
Results
Mean 6.5, median 7, mode 7, range 9 (10 values)
- 3
- 2×
- 4
- 1×
- 5
- 1×
- 7
- 3×
- 8
- 1×
- 9
- 1×
- 12
- 1×
| Step | Working |
|---|---|
| 1. Sort the values | 3, 3, 4, 5, 7, 7, 7, 8, 9, 12 |
| 2. Count them | n = 10 |
| 3. Mean: add, then divide by n | 7 + 3 + 9 + 4 + 7 + 12 + 5 + 7 + 3 + 8 = 65; 65 ÷ 10 = 6.5 |
| 4. Median: the middle value | There are 10 values (even), so the median is the mean of the 5th and 6th values: (7 + 7) ÷ 2 = 7 |
| 5. Mode: the most common value | 7 appears 3 times; 3 appears 2 times. 7 appears most often (3 times), so the mode is 7 |
| 6. Range: largest − smallest | 12 − 3 = 9 |
Read 10 values.
How to use the calculator
- Type or paste your numbers, separated by commas, spaces or new lines. Negative numbers and decimals are fine.
- Read the four answers at the top, then the step-by-step working underneath.
- Use the bar chart to see at a glance which value appears most often.
Formulas and rules
Median = the middle value of the sorted list; with an even count, the mean of the two middle values
Position of the median = (n + 1) ÷ 2
Mode = the value that appears most often (there can be several, or none)
Range = largest value − smallest value
The mean is what most people call the average. The median splits the sorted list in half: as many values lie below it as above. The mode is the most common value, and it is the only one of the three that works for categories such as favorite colors. The range measures spread rather than center: how far apart the extremes are.
Worked example
Find the mean, median, mode and range of 7, 3, 9, 4, 7, 12, 5, 7, 3, 8.
- Sort: 3, 3, 4, 5, 7, 7, 7, 8, 9, 12. There are n = 10 values.
- Mean: the values add up to 65, so the mean is 65 ÷ 10 = 6.5.
- Median: with 10 values (an even number), the middle two are the 5th and 6th, 7 and 7. The median is (7 + 7) ÷ 2 = 7.
- Mode: 3 appears 2 times, 7 appears 3 times; every other value appears once. The mode is 7.
- Range: 12 − 3 = 9.
How the measures compare
Each row below was worked out with the same code the calculator uses. Notice what a single large value does in the second row.
| Data | Values | Mean | Median | Mode | Range |
|---|---|---|---|---|---|
| Five salaries (thousands) | 30, 32, 35, 38, 40 | 35 | 35 | none | 10 |
| Add one salary of 250 | 30, 32, 35, 38, 40, 250 | 70.83 | 36.5 | none | 220 |
| Shoe sizes in a class | 6, 7, 7, 8, 8, 8, 9, 10 | 7.875 | 8 | 8 | 4 |
| Quiz scores out of 10 | 4, 6, 6, 7, 9, 9, 10 | 7.286 | 7 | 6 and 9 | 6 |
Adding one salary of 250 more than doubles the mean, from 35 to 70.83, while the median only moves from 35 to 36.5. That is why house prices and incomes are usually reported as medians. For shoe sizes, the mode is the most useful figure: a shop wants to know the most common size, not an "average" size of 7.875.
Which one should you use?
- Mean: for data without extreme values, and when every value should count, such as test averages.
- Median: when the data is skewed or has outliers, such as incomes, house prices or waiting times.
- Mode: for the most common choice or category, or for whole-number data like sizes.
- Range: for a quick sense of spread; for a measure that is not thrown by one extreme value, use the interquartile range or standard deviation.
Common mistakes
- Forgetting to sort before finding the median. The middle of the unsorted list is not the median.
- Missing repeated values. Write every value, including repeats, when you sort; dropping one changes the count, the mean and possibly the median.
- Counting the mode wrongly. If every value appears once there is no mode; if two values tie for most often, both are modes.
- Giving the range as "3 to 12". The range is a single number: 12 − 3 = 9.
For weighted averages and "what do I need on the final?" questions, use the average calculator. For quartiles, standard deviation and outliers, the statistics calculator gives the full picture.
Frequently asked questions
How do you find the mean of a set of numbers?
Add all the numbers and divide by how many there are. For 7, 3, 9, 4, 7, 12, 5, 7, 3 and 8, the sum is 65 and there are 10 numbers, so the mean is 65 ÷ 10 = 6.5.
How do you find the median when there is an even number of values?
Sort the values and take the mean of the two in the middle. For 3, 5, 8, 10 the middle two are 5 and 8, so the median is (5 + 8) ÷ 2 = 6.5. With an odd count, the median is simply the middle value.
Can a data set have more than one mode, or none?
Yes. In 1, 1, 2, 2, 3 both 1 and 2 appear twice, so there are two modes (bimodal). If every value appears only once, as in 4, 7, 9, there is no mode.
How do you find the range?
Subtract the smallest value from the largest. For 7, 3, 9, 4, 7, 12, 5, 7, 3 and 8, the range is 12 − 3 = 9. The range uses only two values, so a single unusual number can make it much larger.
Which is better, the mean or the median?
The median is better when there are outliers or the data is skewed. Salaries of 30, 32, 35, 38, 40 and 250 (thousand) have a mean of about 70.8 but a median of 36.5, which describes the typical person far better.