Mean, Median and Mode Calculator
Separate values with commas, spaces, semicolons or new lines. Use a point for decimals (7.5). A comma always separates values, so 7,5 is read as 7 and 5.
Mean:
Median:
Mode:
Range:
Calculation:
Paste or type a list of numbers and this calculator gives you the mean, median, mode and range, with every step shown. If there are several modes it lists them all, and if no value repeats it tells you there is no mode.
Below you will find the formulas, solved examples, how to type the list and answers to frequent questions.
How to use the mean, median and mode calculator?
Step 1: Type or paste your values in the box. You do not need to sort them: the calculator sorts them for you.
Step 2: Separate them with commas, spaces, semicolons or new lines. Use a point for decimals.
Step 3: Press Calculate. The results also update as you type.
Step 4: The Calculation box shows the sorted list, the sum, the position of the median and how many times the mode appears.
How to type the list
In English a comma separates values and a point marks decimals. These are the rules the calculator follows:
- Commas, spaces, semicolons and new lines always separate values.
- Decimals use a point: 7.5 is seven and a half.
- A comma is never a decimal mark here, so 7,5 is read as two values, 7 and 5.
- Do not use commas as thousands separators: 1,000 would be read as 1 and 0.
| You type | The calculator reads |
|---|---|
8 7.5 9 | 8, 7.5, 9 |
8, 7.5, 9 | 8, 7.5, 9 |
8;7.5;9 | 8, 7.5, 9 |
8,7,9 | 8, 7, 9 |
7,5 | 7, 5 |
Mean, median, mode and range formulas
Mean
The mean (or average) adds all the values and divides by how many there are:
| mean = (x1 + x2 + ... + xn) ÷ n |
Median
The median is the value in the middle when the data are sorted. With an odd count it is the middle value. With an even count it is the average of the two middle values.
Mode
The mode is the value that appears most often. There can be more than one mode, and if no value repeats there is no mode.
Range
The range measures how spread out the data are: it is the difference between the largest and the smallest value.
| range = maximum value - minimum value |
Mean, median and mode examples
Example 1: An odd number of values
Data: 4, 8, 6, 5, 3, 8, 9. Sorted: 3, 4, 5, 6, 8, 8, 9.
Mean: 3 + 4 + 5 + 6 + 8 + 8 + 9 = 43, and 43 ÷ 7 ≈ 6.1429
Median: there are 7 values, so it is the one in position 4: 6
Mode: 8 appears 2 times, more than any other value: 8
Range: 9 - 3 = 6
Example 2: An even number of values with decimals
Scores: 7.5, 9, 6, 8.5, 7, 9. Sorted: 6, 7, 7.5, 8.5, 9, 9.
Mean: 6 + 7 + 7.5 + 8.5 + 9 + 9 = 47, and 47 ÷ 6 ≈ 7.8333
Median: there are 6 values, so we average positions 3 and 4: (7.5 + 8.5) ÷ 2 = 8
Mode: 9 appears 2 times: 9
Range: 9 - 6 = 3
Example 3: Two modes and no mode
In 2, 3, 3, 5, 5, 8, 3 and 5 each appear 2 times, so there are two modes: 3 and 5. This is called a bimodal set.
In 1, 2, 3, 4 no value repeats, so there is no mode. The mean is 2.5 and the median is 2.5.
Example 4: When the median beats the mean
Five orders took 3, 4, 4, 5, 30 days to arrive. A single very late order pulls the mean up:
Mean: 3 + 4 + 4 + 5 + 30 = 46, and 46 ÷ 5 = 9.2 days
Median: the middle value is 4 days
The mean (9.2 days) does not describe most of the orders, but the median (4 days) does. When there are extreme values, the median is a better picture of the typical case.
Summary of the measures
Using the data from example 1 (3, 4, 5, 6, 8, 8, 9):
| Measure | What it tells you | Result |
|---|---|---|
| Mean | The average value | 6.1429 |
| Median | The middle value | 6 |
| Mode | The most frequent value | 8 |
| Range | How spread out the data are | 6 |
Frequently asked questions
What is the difference between mean, median and mode?
The mean is the average of all values, the median is the middle value and the mode is the value that appears most often. For 4, 8, 6, 5, 3, 8, 9 they are 6.1429, 6 and 8.
When should I use the mean and when the median?
Use the mean when the values are similar to each other. Use the median when a few very high or very low values distort the average, as in example 4, where the mean is 9.2 and the median is 4.
What if there are two modes or none?
If two or more values tie for the most repeats, all of them are modes, like 3 and 5 in example 3. If no value repeats, there is no mode.
How do you find the median with an even number of values?
Sort the values and average the two in the middle. For 2, 3, 3, 5, 5, 8, the middle values are 3 and 5, and their average is 4.
Do I have to sort the data before using the calculator?
No. The calculator sorts it for you and shows the sorted list in the Calculation box.
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