What Is Mean, Median, Mode and Range?
The mean is the average, the median is the middle value when the data are sorted, the mode is the most frequent value and the range is the difference between the largest and smallest values. Together they describe the centre and basic spread of a small data set, and they are the four statistics taught first in most courses.
Enter your numbers separated by commas, spaces or new lines. The calculator sorts the data, shows how the median is found for odd and even counts, lists every mode when there is more than one, and compares the mean with the median to hint at skew.
Below you will find the formulas, a variables table, worked examples and answers to common questions such as what to do when there is no mode or two modes.
How to Use the Mean, Median, Mode and Range Calculator
- Type or paste your numbers, separated by commas, spaces or new lines.
- Read the mean, median, mode and range in the results.
- Open the step-by-step solution to see how each one was worked out.
Mean, Median, Mode and Range Formula
Mean
Median (odd n)
Median (even n)
Range
| Measure | Best for | Affected by outliers? |
|---|---|---|
| Mean | Symmetric data, further calculations | Yes, strongly |
| Median | Skewed data such as incomes or house prices | No |
| Mode | Categories and most common values | No |
Mean, Median, Mode and Range Variables Explained
| Symbol | Meaning | Notes |
|---|---|---|
| x̄ | Mean | Sum ÷ count |
| n | Number of values | |
| Median | Middle value | Average of the two middle values if n is even |
| Mode | Most frequent value | There can be none, one or several |
| Range | Maximum − minimum |
Mean, Median, Mode and Range Worked Example
With the example values loaded in the calculator above, the steps are:
- Sort the data: 2, 3, 4, 7, 7, 7, 9, 10.
- Mean = sum ÷ count = 49 ÷ 8 = 6.125.
- Median = the average of the two middle values, 7 and 7, which is 7.
- Mode = 7 (appears 3 times).
- Range = max − min = 10 − 2 = 8.
Result: Mean = 6.125; Median = 7; Mode = 7 (appears 3 times); Range = 8.
Worked Example: 3, 7, 7, 2, 9, 4, 10, 7
Sorted, the eight values are 2, 3, 4, 7, 7, 7, 9, 10. They add to 49, so the mean is 49 ÷ 8 = 6.125. The median is the middle of the two central values, both 7, so it is 7. The mode is 7, which appears three times. The range is 10 − 2 = 8.
Here the mean is slightly below the median, which is a hint of left skew, but with only eight values it is weak evidence. A data set can have no mode, one mode or several, and the median stays the same if the 10 is changed to 100, while the mean would jump to 17.4. That robustness is the reason to look at both.
Worked example
Take the data 3, 7, 7, 2, 9, 4, 10, 7. Sorted it reads 2, 3, 4, 7, 7, 7, 9, 10. The sum is 49 and there are 8 values, so the mean is 49 ÷ 8 = 6.125. With an even count the median is the average of the two middle values, 7 and 7, which is 7. The value 7 appears three times, so the mode is 7. The range is 10 − 2 = 8.
Notice that the mean (6.125) is below the median (7). That small gap, together with the low outlier 2, hints at slight left skew.
Which average should you use?
“Average” usually means the mean, but it is not always the best summary. Choose the measure that matches your data and your question.
| Mean | Median | Mode | |
|---|---|---|---|
| Definition | Sum ÷ count | Middle value | Most common value |
| Works for | Numeric data | Ordered data | Any data, including categories |
| Outliers | Pulled strongly | Resistant | Resistant |
| Always exists | Yes | Yes | May be none or several |
| Best example | Test scores, temperatures | House prices, incomes | Shoe size, favourite colour |
Reading skew from mean and median
In symmetric data the mean and median are nearly equal. When a long tail pulls the mean toward it, the mean moves away from the median: mean greater than median means right skew (income distributions), mean less than median means left skew. The results panel flags this for your data.
Range, quartiles and spread
The range is simple but depends on only two values, so one outlier changes it a lot. The interquartile range (Q3 − Q1) describes the middle half of the data and ignores extremes, and the box plot draws it for you with outliers marked as separate points.
Where Mean, Median, Mode and Range Is Used
Homework
Find all four basic statistics for a list of numbers at once.
Skew check
Compare the mean and median to see which way the data lean.
Quartiles
See Q1, Q3 and the IQR with the range.
Checking a frequency table
See how often each value occurs.
Common Mean, Median, Mode and Range Mistakes to Avoid
- Not sorting before finding the median.
- Forgetting to average the two middle values when the count is even.
- Reporting a mode when no value repeats; there is none.
- Using the mean for heavily skewed data such as incomes.
- Mixing up the range with the interquartile range.
- A data set can have one mode, several modes, or none at all.
- When the mean and median are far apart, the data is probably skewed.
- The range uses only two values, so a single outlier can change it a lot.
Mean, Median, Mode and Range Terms and Definitions
- Mean
- The arithmetic average: sum divided by count.
- Median
- The middle value of ordered data.
- Mode
- The value that occurs most often; there can be several.
- Range
- Largest minus smallest value.
- Quartile
- One of the three values that split ordered data into four equal parts.
- Outlier
- A value far from the rest of the data.
Mean, Median, Mode and Range FAQs
How do you find the mean, median, mode and range?
Mean: add and divide by the count. Median: sort and take the middle (or average the two middle values). Mode: find the most frequent value. Range: subtract the smallest from the largest.
What if there is no mode?
If every value appears once, the data has no mode. If several values tie, they are all modes.
What is the difference between average and mean?
In everyday use “average” means the mean. Strictly, mean, median and mode are all averages (measures of central tendency).
Which is better, mean or median?
Use the mean for roughly symmetric data and the median for skewed data or data with outliers.
How do I find the median of an even number of values?
Average the two middle values after sorting.
Does this calculator work for decimals and negatives?
Yes. Enter any real numbers separated by commas, spaces or new lines.
What is the midrange?
The midpoint between the smallest and largest values. It is quick but very sensitive to outliers.
How do you find the median?
Sort the numbers. If there is an odd count, the median is the middle one. If the count is even, it is the average of the two middle numbers.
Can there be more than one mode?
Yes. If two or more values tie for the highest frequency, all of them are modes. If every value appears once, there is no mode.
What is the difference between mean and median?
The mean is the sum divided by the count. The median is the middle value of the sorted list. The median is less sensitive to extreme values.
What is the range?
The range is the largest value minus the smallest value. It is the simplest measure of spread.
When is the median better than the mean?
When the data has outliers or a long tail. In the sample 3, 7, 7, 2, 9, 4, 10, 7 the mean is 6.125 and the median is 7. Income and house prices are classic cases where the median describes a typical value better.
What if there is more than one mode or no mode?
Data can have several modes when values tie for most frequent, and no mode when every value appears once. In 3, 7, 7, 2, 9, 4, 10, 7 the mode is 7, which appears 3 times.
How do I find the range?
Subtract the smallest value from the largest. Here 10 − 2 = 8. The range uses only two values, so one outlier changes it a lot; the IQR is steadier.
How is the median found with an even number of values?
Sort the values and average the two middle ones. With 8 values the median is the mean of the 4th and 5th sorted values.