Median Calculator

Find the middle value of your dataset with step-by-step solution

Calculate Median

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Example Calculations

Example 1: Odd Number of Values

Data: 58, 47, 55, 6, 5, 14, 60, 3, 39, 6, 28, 15, 87, 31, 19 (15 values)

Sorted: 3, 5, 6, 6, 14, 15, 19, 28, 31, 39, 47, 55, 58, 60, 87

Position: (15 + 1) ÷ 2 = 8th position

Median: 28 (the 8th value in the sorted list)

Example 2: Even Number of Values

Data: 71, 71, 5, 18, 98, 23, 53, 92, 74, 82, 65, 74, 97, 75, 87, 13 (16 values)

Sorted: 5, 13, 18, 23, 53, 65, 71, 71, 74, 74, 75, 82, 87, 92, 97, 98

Positions: 8th and 9th values (71 and 74)

Median: (71 + 74) ÷ 2 = 72.5

Example 3: Small Dataset

Data: 0, 1, 1, 18 (4 values)

Sorted: 0, 1, 1, 18

Positions: 2nd and 3rd values (both are 1)

Median: (1 + 1) ÷ 2 = 1

Median Properties

🎯
Middle Value
50% of data above, 50% below
🛡️
Outlier Resistant
Not affected by extreme values
⚖️
Robust Measure
Better for skewed distributions
📊
Percentile
Equivalent to 50th percentile

Median vs Mean

Use Median When:
• Data has outliers
• Distribution is skewed
• Need robust measure
Use Mean When:
• Data is symmetric
• No extreme outliers
• Normal distribution

Median Symbols

Most common
MSimple notation
μ₁/₂50th percentile
Q₂Second quartile

Understanding the Median

What is the Median?

The median is the middle value of a dataset when arranged in ascending order. It divides the data into two equal halves: 50% of values are below the median, and 50% are above it.

Why Use the Median?

  • Less affected by extreme values (outliers) than the mean
  • Better represents "typical" value in skewed distributions
  • Useful for income data, test scores, and other real-world datasets
  • Provides a robust measure of central tendency

Calculation Methods

Odd Number of Values
Median = x((n+1)/2)
Take the middle value directly
Even Number of Values
Median = (x(n/2) + x((n/2)+1)) / 2
Average the two middle values

Remember: Always sort your data first before finding the median!

Real-World Applications

💰 Income Analysis

Median household income is preferred over mean income because it's not skewed by extremely high earners.

Example: $35K, $40K, $45K, $1M
Mean: $280K, Median: $42.5K

🏠 Real Estate

Median home prices provide a better sense of the typical home value in an area.

Helps buyers understand
realistic price expectations

📊 Test Scores

Median test scores show the performance of the "middle" student, unaffected by very high or low scores.

Fair representation of
class performance