Mean, Median, Mode, Range Calculator
Calculate the most common statistical averages and view a visual column chart of your dataset.
Descriptive Statistics
Mean, Median, Mode, and Range Calculator
A Mean, Median, Mode, and Range Calculator helps analyze a set of numbers quickly. It calculates the average value, middle value, most repeated value, and the difference between the largest and smallest numbers.
Definitions
What Are Mean, Median, Mode, and Range?
These four values summarize a data set. Each one explains a different part of the data.
- Mean
- The average of all numbers. Add the values and divide by the count.
- Median
- The middle value when the numbers are arranged from smallest to largest.
- Mode
- The number that appears most often in the data set.
- Range
- The difference between the largest and smallest number.
How to Use
How to Use the Calculator
The calculator accepts a list of numbers and returns the most common descriptive statistics.
- 1
Enter the data
Type values separated by commas, spaces, semicolons, or new lines.
- 2
Calculate metrics
The calculator sorts the data and finds the mean, median, mode, range, sum, count, minimum, and maximum.
- 3
Review the chart
The result view shows a visual column chart so the values are easier to compare.
The Math
Mean Formula
The mean is the arithmetic average of all values.
Mean
Example: for 4, 7, 7, 9, 10, 12, 12, 12, 15, the sum is 88 and the count is 9, so the mean is 88 / 9 = 9.78.
The Math
Median Formula
The median is the middle number in a sorted data set. If the count is even, it is the average of the two middle values.
Odd number of values
Example: in 4, 7, 7, 9, 10, 12, 12, 12, 15, the fifth number is 10, so the median is 10.
Even number of values
Example: for 3, 6, 8, 12, the two middle values are 6 and 8, so the median is 7.
The Math
Mode
The mode is the value that appears most often. A data set can have no mode, one mode, or multiple modes.
| Case | Data set | Result |
|---|---|---|
| One mode | 4, 7, 7, 9, 10, 12, 12, 12, 15 | 12 appears three times |
| No mode | 2, 4, 6, 8 | No number repeats |
| Multiple modes | 2, 2, 4, 4, 6 | 2 and 4 both appear twice |
The Math
Range Formula
The range shows the quick spread between the smallest and largest values.
Range
Example: for 4, 7, 7, 9, 10, 12, 12, 12, 15, the range is 15 - 4 = 11.
Interpretation
Mean vs. Median vs. Mode vs. Range
Use all four values together to understand the center, frequency, and spread of the data.
| Metric | How it works | Sensitive to outliers? | Best use |
|---|---|---|---|
| Mean | Adds all values and divides by count | Affected by very high or very low values | Balanced data |
| Median | Finds the middle value | Less affected by extreme values | Skewed data or outliers |
| Mode | Finds the most repeated value | Only depends on frequency | Most common score, item, or category |
| Range | Subtracts smallest value from largest value | Only uses the endpoints | Quick spread estimate |
Example
Why These Statistics Are Useful
Mean, median, mode, and range help summarize a list of numbers in a way that is easier to compare.
| Calculation | KaTeX form | Result |
|---|---|---|
| Mean example | 9.78 | |
| Even median example | 7 | |
| Range example | 11 |
Frequently Asked Questions
It calculates the average, middle value, most common value, and spread of a set of numbers.
The mean is the average. Add all numbers together and divide by the number of values.
The median is the middle value when all numbers are arranged from smallest to largest.
The mode is the number that appears most often in a data set.
The range is the difference between the largest and smallest number.
Yes. If two or more numbers appear the same highest number of times, the data set has multiple modes.
Yes. If no number repeats, there is no mode.
It depends on the data. Mean is useful for balanced data. Median is often better when there are very high or very low values.
Use this formula: Range = Maximum Value - Minimum Value.
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