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Median Calculator

The median is the physical middle value in an ordered dataset, separating the top 50% from the bottom 50%. This free Median Calculator automatically s

Mathematics
Values will be sorted automatically from lowest to highest.
Formula & Methodology
For Odd Count (n): Median = x_((n + 1) ÷ 2) For Even Count (n): Median = (x_(n ÷ 2) + x_((n ÷ 2) + 1)) ÷ 2

To calculate the median of any dataset: 1. Arrange all numbers in ascending order from smallest to largest. 2. If the total count n is odd, the median is the single value sitting precisely at position (n + 1) / 2. 3. If the total count n is even, there is no single middle number; average the two center numbers sitting at positions (n / 2) and (n / 2 + 1).

Median of 7 Sorted Values

15

Overview

The median is the physical middle value in an ordered dataset, separating the top 50% from the bottom 50%. This free Median Calculator automatically sorts your dataset, determines whether the count is odd or even, calculates the exact median, and displays the full five-number quartile distribution.

Unlike the arithmetic mean, the median is immune to extreme outliers. That makes it the preferred gold standard for reporting real-world metrics like household incomes, real estate home sales prices, and surgical recovery timelines.

Worked Examples

Example 1: Odd Count Dataset [3, 7, 12, 15, 18, 21, 29]

Dataset: 7 numbers (Odd count)

  1. Confirm sorted order: 3, 7, 12, 15, 18, 21, 29.
  2. Middle position: (7 + 1) ÷ 2 = position 4.
  3. Value at position 4 is 15.
Final Answer: 15.00

Example 2: Even Count Dataset [10, 14, 18, 22, 26, 32]

Dataset: 6 numbers (Even count)

  1. Confirm sorted order: 10, 14, 18, 22, 26, 32.
  2. Identify two center values at positions 3 and 4: 18 and 22.
  3. Average the two centers: (18 + 22) ÷ 2 = 40 ÷ 2 = 20.
Final Answer: 20.00

Example 3: Home Prices with Outlier [$300k, $320k, $350k, $380k, $2.5M]

Dataset: 300, 320, 350, 380, 2500

  1. The massive $2.5M mansion pulls the mean up to $770,000.
  2. The median remains stable at the true middle home: $350,000.
Final Answer: $350,000 (Resistant to outlier)

How to Use This Calculator

  1. Paste your dataset separated by commas or spaces.
  2. Click "Calculate" to sort the numbers and find the median.
  3. View the sorted array, sample count, Q1, Q3, and IQR below.
  4. Click "Reset" to compute the median for another dataset.

Reference Table

DatasetSorted OrderCount (n)Median
8, 2, 52, 5, 83 (Odd)5.00
4, 1, 9, 71, 4, 7, 94 (Even)5.50
12, 3, 8, 15, 11, 3, 8, 12, 155 (Odd)8.00
20, 10, 40, 3010, 20, 30, 404 (Even)25.00
3, 7, 12, 15, 18, 21, 293, 7, 12, 15, 18, 21, 297 (Odd)15.00

Frequently Asked Questions

Why is the median preferred over the mean for income and home prices?
Income and real estate distributions are heavily right-skewed by billionaires and multi-million dollar luxury estates. The median reflects what a typical resident or home buyer actually experiences.
What is the Interquartile Range (IQR)?
The IQR is the distance between the 75th percentile (Q3) and 25th percentile (Q1): IQR = Q3 - Q1. It measures the spread of the middle 50% of your data.
Can the median be a number not present in the original dataset?
Yes. When the dataset has an even count, the median is the average of the two middle values, which may not be in the original list (e.g. median of 4 and 6 is 5).
Does the calculator require pre-sorted numbers?
No. The calculator automatically sorts your numbers in ascending order before performing any calculations.
What is the relationship between mean and median in a symmetric distribution?
In a perfectly symmetric bell curve (normal distribution), the mean, median, and mode are exactly equal.

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Reviewed & Authored by: Dr. Elizabeth Vance, PhD Applied Mathematics · Last Updated: 2026-10-06
Computed via comparison-based quicksort and order statistic rank selection.