Median Calculator
Find the middle value of your data set. The median is resistant to outliers and provides a better measure of central tendency for skewed data.
Result
- Number of Values
- 0
- Sorted Values
- -
- Median
- 0
Formula & Guide
Formula
M
Odd Number of Values
Median = Middle Value
Take the value at position (n+1)/2
M
Even Number of Values
Median = (Value₁ + Value₂) / 2
Average of the two middle values
Formula Variables
n
Count
The total number of values in the sorted dataset
Value₁, Value₂
Middle Values
The two middle values when n is even (at positions n/2 and n/2+1)
Median
Median
The middle value that divides the dataset into two equal halves
Step-by-Step Scenario
Example Scenario
Values
10, 20, 30, 40, 50
1
Sort the Values
- Values are already sorted: 10, 20, 30, 40, 50
Always sort values from smallest to largest first
2
Find the Middle Position
- With 5 values, the middle position is (5+1)/2 = 3rd position
3
Identify the Median
- Position 3: 30
Additional Examples
Even Count
Values: 10, 20, 30, 40
Sorted
10, 20, 30, 40
Middle Values
20 and 30
Median
(20 + 30) / 2 = 25
With Outliers
Values: 1, 2, 3, 4, 100
Mean
(1+2+3+4+100)/5 = 22
Median
3 (less affected by outlier)
Characteristics of Median
Resistant to Outliers
The median is not affected by extreme values. A single outlier won't change the median, making it ideal for skewed data.
Robust Measure
Unlike the mean, the median provides a stable measure of central tendency even when data contains outliers or is non-normally distributed.
Common Use Cases
Used for income data, house prices, test scores, and any dataset where outliers might skew the mean unfairly.
Simple Calculation
Easy to understand and calculate: just sort and find the middle. No complex formulas needed.
Important Notes
- The median requires sorting the data first. Always arrange values from smallest to largest before finding the median.
- For odd counts, the median is a single value. For even counts, the median is the average of two values, which can be a decimal.
- The median divides the dataset into two equal halves: 50% of values are below the median, 50% are above.
- Unlike the mean, the median is not affected by the magnitude of outliers, only by their position in the sorted list.
- The median is particularly useful for ordinal data (ranked data) and when the mean would be misleading due to skewness.
Frequently Asked Questions
Find answers to common questions about median calculations.