# What are the mean, median, mode?

Computes the mean, median, and mode of a list of numbers, with the count, sum, smallest and largest value, and range.

- Page: https://www.acalculator.org/statistics/mean-median-mode-calculator
- JSON spec: https://www.acalculator.org/statistics/mean-median-mode-calculator.json
- Version: c5554c3fe1ff

## Default answer

Example with the default inputs (Your numbers [1, 2, 3, 4, 5, 5, 6, 6, 6, 6, 7, 8, 9]): For 1, 2, 3, 4, 5, 5, 6, 6, 6, 6, 7, 8, 9, the mean is 5.230769 and the median is 6 (mode: 6).

## Inputs

| Key | Label | Description |
| --- | --- | --- |
| input | Your numbers | The numbers, separated by commas, spaces, semicolons, or new lines. |

## Outputs

| Key | Label | Description |
| --- | --- | --- |
| mean | Mean | The average: the sum divided by how many numbers there are. |
| median | Median | The middle value in sorted order; the average of the two middle values when the count is even. |
| mode | Mode | The value or values that occur most often, or No mode when no value repeats. |
| modeFrequency | Times the mode occurs | How many times each mode appears in the list. Shown only when there is a mode. |
| count | Count | How many numbers are in the list. |
| sum | Sum | All the numbers added up. |
| min | Smallest | The smallest number in the list. |
| max | Largest | The largest number in the list. |
| range | Range | The largest number minus the smallest. |

## Method

mean = sum ÷ count; median = the middle sorted value (the average of the two middle values for an even count); mode = the most frequent value or values.

## Assumptions

- Every number in the list counts once. The order of the list does not change any result.
- When no value occurs more than once there is no mode. When several values tie for most often, all of them are modes.

## Worked examples

1. input = 1 or 2 gives mean = 5.230769, median = 6, mode = 6, modeFrequency = 4, count = 13, sum = 68, min = 1, max = 9, range = 8. Source: NIST/SEMATECH e-Handbook of Statistical Methods, §1.3.5.1 Measures of Location (mean, median, mode). https://www.itl.nist.gov/div898/handbook/eda/section3/eda351.htm.
2. input = 1 or 2 gives mean = 2.4, median = 2, mode = 2, modeFrequency = 2. Source: NIST/SEMATECH e-Handbook of Statistical Methods, §1.3.5.1 Measures of Location (mean, median, mode). https://www.itl.nist.gov/div898/handbook/eda/section3/eda351.htm.
3. input = 1 or 2 gives mean = 2.5, median = 2.5, mode = No mode, range = 3. Source: NIST/SEMATECH e-Handbook of Statistical Methods, §1.3.5.1 Measures of Location (mean, median, mode). https://www.itl.nist.gov/div898/handbook/eda/section3/eda351.htm.
4. input = 1 or 1 gives mean = 1.8, median = 2, mode = 1, 2, modeFrequency = 2. Source: NIST/SEMATECH e-Handbook of Statistical Methods, §1.3.5.1 Measures of Location (mean, median, mode). https://www.itl.nist.gov/div898/handbook/eda/section3/eda351.htm.

## FAQ

### What is the difference between mean, median, and mode?

The mean is the average of all numbers (sum divided by count). The median is the middle value when numbers are arranged in order. The mode is the number that appears most frequently. For example, in the set [1, 2, 2, 3, 4]: Mean = 2.4, Median = 2, Mode = 2.

### How do I enter numbers in the calculator?

You can separate numbers with commas (1,2,3,4), spaces (1 2 3 4), semicolons (1;2;3;4), new lines, or a mix of these.

### What happens if I enter invalid numbers?

The calculator names the first entry that is not a number, for example "a" is not a number, and shows no result until you fix it. It does not skip entries silently.

### Can I have multiple modes?

Yes! If multiple numbers appear the same number of times (and more frequently than any other number), they are all considered modes. For example, in [1, 1, 2, 2, 3], both 1 and 2 are modes.

### What if there is no mode?

If no number appears more than once, there is no mode. The calculator will display 'No mode' in this case.

### How is the median calculated for an even number of values?

For an even number of values, the median is the average of the two middle numbers. For example, in [1, 2, 3, 4], the median is (2 + 3) ÷ 2 = 2.5.

### Which measure of central tendency should I use?

Use the mean for normally distributed data, the median when there are outliers that could skew the mean, and the mode for categorical data or when you want to know the most common value.

### Can I use decimal numbers?

Yes! The calculator supports both whole numbers and decimal numbers. Examples: 1.5, 2.75, 3.14159, etc.

### What additional statistics does the calculator show?

Besides mean, median, and mode, the calculator also shows: count (number of values), sum, minimum value, maximum value, and range (max - min).

### Is there a limit to how many numbers I can enter?

There's no strict limit, but for best performance, we recommend entering up to 10,000 numbers. The calculator can handle large datasets efficiently.

## Sources

- NIST/SEMATECH e-Handbook of Statistical Methods, §1.3.5.1 Measures of Location (mean, median, mode). https://www.itl.nist.gov/div898/handbook/eda/section3/eda351.htm