Median Calculator

Understanding the Median

The median is a measure of central tendency that represents the middle value in a dataset. It's the value that separates the higher half from the lower half of your data.

How to Calculate Median

1. Arrange all numbers in ascending order
2. If the count is odd: The median is the middle number
3. If the count is even: The median is the average of the two middle numbers

Example Calculations

Odd Count Example

• Original: 5, 1, 9, 3, 7
• Sorted: 1, 3, 5, 7, 9
• Median: 5 (the middle value)

Even Count Example

• Original: 4, 1, 8, 2
• Sorted: 1, 2, 4, 8
• Two middle values: 2 and 4
• Median: (2 + 4) / 2 = 3

Median vs Mean (Average)

• Mean: Sum of all values ÷ count. Affected by extreme values.
• Median: Middle value. Resistant to outliers.
• Example with outlier: [1, 2, 3, 4, 100]
• Mean = 22 (skewed by 100)
• Median = 3 (better represents typical value)

When to Use Median

• Income/Salary Data: A few high earners skew the mean
• Home Prices: Luxury homes inflate the average
• Test Scores: When a few very high or low scores exist
• Skewed Distributions: When data is not symmetrical
• Ordinal Data: Data that can be ranked but differences aren't meaningful

Properties of Median

• Always exists for any dataset with at least one value
• Not affected by extreme values (robust statistic)
• Represents the 50th percentile
• May or may not be a value from the original dataset
• For symmetric distributions, median ≈ mean
• For right-skewed distributions, median < mean
• For left-skewed distributions, median > mean