What is Median?

The median is the middle value in a sorted dataset. It divides the data into two equal halves and is less affected by extreme values (outliers) than the mean.

For odd count: Median = middle value
For even count: Median = average of two middle values

Example

Dataset: 3, 7, 1, 9, 4 → Sorted: 1, 3, 4, 7, 9 → Median = 4 (middle value)

Dataset: 2, 4, 6, 8 → Median = (4 + 6) / 2 = 5 (average of two middles)

Median for Odd vs Even Count

Odd count (n=5): Median = value at position (n+1)/2 = 3rd value
Even count (n=6): Median = average of values at positions n/2 and n/2+1

Example odd: {3, 7, 12, 18, 25} → Median = 12 (3rd value)
Example even: {4, 8, 11, 15, 20, 30} → Median = (11+15)/2 = 13

Median vs Mean — When They Differ

When mean and median are far apart, it signals a skewed distribution:

Scenario	Mean	Median	Better Measure
Salaries: $30k,35k,32k,40k,$500k (CEO)	$127.4k	$35k	Median
Home prices with luxury mansion	Inflated	Typical	Median
Test scores (no outliers)	Fair	Fair	Either
Symmetric bell curve	= Median	= Mean	Either

Quartiles and Percentiles

The median is the 50th percentile (Q₂). Quartiles divide sorted data into 4 equal parts:

Q1 (25th percentile) = median of lower half
Q2 (50th percentile) = median of whole dataset
Q3 (75th percentile) = median of upper half
IQR (Interquartile Range) = Q3 − Q1

Real-World Uses of Median

Housing market: Median home price is the standard measure (not mean, which is skewed by mansions)
Household income: Government statistics use median income to represent a "typical" household
Medical research: Median survival time in clinical trials
Education: Standardized test score percentiles (SAT, GRE)

Median Calculator