Mean, Median, Mode & Range Calculator
Calculate statistical averages from a dataset.
Basic Statistics
Calculate mean, median, mode, range, and other basic statistics
Quick Tips
- • Mean is the average of all values
- • Median is the middle value when sorted
- • Mode is the most frequent value
- • Range shows the spread of data
What Do Mean, Median, Mode, and Range Mean?
These are common ways to summarize a set of numbers:
- Mean: average value
- Median: middle value after sorting
- Mode: most frequent value
- Range: highest minus lowest
Quick Definitions (One-Liners)
| Measure | What it tells you | Best for |
|---|---|---|
| Mean | Overall average | Balanced data without extreme outliers |
| Median | Middle of the dataset | Skewed data or data with outliers |
| Mode | Most common value | Most frequent category/value |
| Range | Spread (max − min) | Quick sense of variability |
Formulas
Mean: (x₁ + x₂ + ... + xₙ) / n
Median: middle value after sorting (or average of two middle values if n is even)
Mode: value(s) with highest frequency
Range: max(x) − min(x)
How the Calculator Works (Step-by-Step)
- 1Clean the input list (remove spaces and invalid entries).
- 2Sort numbers from smallest to largest.
- 3Compute mean = sum / count.
- 4Find median: if count is odd → middle number; if even → average of two middle numbers.
- 5Find mode: count frequencies and pick the most frequent value(s).
- 6Compute range = max − min.
Worked Example (Odd Count)
| Dataset | Mean | Median | Mode | Range |
|---|---|---|---|---|
| 10, 20, 20, 30, 50 | 26 | 20 | 20 | 40 |
Worked Example (Even Count)
| Dataset | Sorted | Mean | Median | Mode | Range |
|---|---|---|---|---|---|
| 2, 4, 8, 10 | 2, 4, 8, 10 | 6 | 6 (avg of 4 and 8) | No mode | 8 |
Mode note: Some datasets have no mode (all values appear once). Some have multiple modes (two or more values tied for highest frequency).
Mean vs Median (Outliers Matter)
The mean is sensitive to extreme values (outliers). The median is often better when data is skewed.
Example: 1, 2, 2, 3, 100 → mean gets pulled up, but median stays near the center.
Visual: Outlier Pulls the Mean
When to Use Which Measure
- Use mean for balanced datasets (no extreme outliers).
- Use median for income, house prices, or skewed distributions.
- Use mode for most common value (popular size, most repeated score).
- Use range for a quick spread check (but it ignores everything in the middle).
Mean Median Mode FAQs
What is the difference between mean and average?
In everyday language, “average” usually means the mean: sum of values divided by count.
How do you find the median with an even number of values?
Sort the list, take the two middle numbers, and average them.
Can a dataset have more than one mode?
Yes. If two or more values tie for the highest frequency, the dataset is multimodal.
What if every number appears only once?
Then the dataset has no mode.
Does the calculator handle decimals and negatives?
Yes. Mean, median, and range work normally with decimals and negative numbers.
Why can mean be misleading?
Because outliers can pull it away from the typical values. Median is often more robust.
Is range enough to describe spread?
Range is a quick summary, but it only uses min and max. For deeper spread, use variance/standard deviation too.
Do you calculate mean before or after sorting?
Sorting is not required for mean, but it is required for median (and helpful for mode checks).