Mean, Median, Mode & Range
These four measures help you describe and summarize a set of numbers. Together they are the foundation of basic statistics.
The Four Measures
Mean
The average. Add all values and divide by how many there are.
Median
The middle value when all numbers are sorted in order.
Mode
The value that appears most often. A data set can have one mode, multiple modes, or no mode.
Range
The spread. Subtract the smallest value from the largest.
Mean (Average)
Add all the numbers together, then divide by the count of numbers.
Example
Data set: 4, 7, 13, 2, 9
Step 1 — Add: 4 + 7 + 13 + 2 + 9 = 35
Step 2 — Count: there are 5 values
Step 3 — Divide: 35 ÷ 5 = 7
Mean = 7
Outliers Skew the Mean
One very large or very small value pulls the mean away from the typical value. If your data set is 1, 2, 3, 4, 100, the mean is 22 — but that does not represent most of the numbers. The median handles this better.
Median (Middle Value)
Sort the numbers from smallest to largest, then find the middle one.
Odd number of values
Data: 3, 7, 1, 9, 4
Sorted: 1, 3, 4, 7, 9
Middle value (position 3 of 5): 4
Median = 4
Even number of values
Data: 5, 2, 8, 4
Sorted: 2, 4, 5, 8
Two middle values: 4 and 5
Average them: (4 + 5) ÷ 2 = 4.5
Median = 4.5
Mode (Most Frequent)
Examples
Data: 3, 5, 3, 7, 3, 8
Mode = 3 (appears 3 times)
Data: 2, 4, 4, 6, 6, 8
Mode = 4 and 6 (both appear twice — bimodal)
Data: 1, 2, 3, 4, 5
Mode = none (all values appear once)
Range (Spread)
Example
Data: 12, 5, 28, 3, 19
Largest = 28, Smallest = 3
Range = 28 − 3 = 25
A large range means the data is spread out. A small range means values are close together.
When to Use Each Measure
| Measure | Best Used When | Avoid When |
|---|---|---|
| Mean | Data has no extreme outliers; normal distribution | One or two extreme values skew the result |
| Median | Data has outliers (e.g., income, house prices) | You need an exact mathematical average |
| Mode | Finding most common category or value (e.g., shoe sizes) | All values are unique (then there is no mode) |
| Range | Describing how spread out data is | You need more detail about the spread |
Quick Quiz
Check your understanding. Click an answer to see if you got it right.