What Is the Median?
The median is the middle value in a sorted list of numbers. It divides a dataset into two equal halves: 50% of the values fall below the median and 50% fall above it. The median is a measure of central tendency, alongside the mean and the mode.
Unlike the arithmetic mean (average), the median is resistant to outliers — extremely high or low values have little effect on the result. This makes it the preferred statistic whenever your dataset is skewed or contains extreme values.
Median vs. Mode
The mode is the value that appears most often in a dataset, while the median is the middle value when data is sorted. For perfectly symmetrical (normal) distributions, the mean, median, and mode are all equal. In skewed distributions, they diverge:
- Right-skewed data (e.g., income): mean > median > mode
- Left-skewed data: mean < median < mode
Journalists and data analysts often prefer the median over the mean for reporting income, house prices, and salaries because a few very high earners can inflate the mean dramatically.
Median Symbol
There is no single universally adopted symbol for the median, but the most commonly used notations are:
- x̃ (x-tilde) — most common in statistics textbooks
- M — used in some introductory statistics courses
- μ1/2 — notation used in advanced probability contexts
- Med(X) — functional notation sometimes used in academic papers
How to Find the Median — Median Formula
To find the median, follow these steps:
- Sort the data in ascending order (smallest to largest).
- Count the values (n).
- Apply the appropriate formula:
- Odd count: Median = value at position (n + 1) / 2
- Even count: Median = average of values at positions n/2 and n/2 + 1
Example: Odd Number of Values
Dataset: 4, 7, 2, 9, 5
Step 1 — Sorted: 2, 4, 5, 7, 9
Step 2 — n = 5 (odd), middle position = (5 + 1) / 2 = 3
Step 3 — Median = 5
Example: Even Number of Values
Dataset: 4, 5, 6, 7
Step 1 — Sorted: 4, 5, 6, 7
Step 2 — n = 4 (even), middle positions = 2 and 3
Step 3 — Median = (5 + 6) / 2 = 5.5
How to Use This Calculator to Find the Median
- Select the unit type — choose Plain Number, Currency, Imperial (US), or Metric measurement.
- If using Currency, select your preferred currency from the list (USD, EUR, GBP, JPY, and 21 more).
- If using Imperial or Metric, choose the specific unit (inches, feet, kilograms, meters, etc.).
- Enter your numbers — type values in the fields. The form automatically expands as you enter more numbers (up to 50).
- Click Calculate — the calculator will sort your data, find the median, and display a full step-by-step explanation with a sorted table highlighting the median value(s).
How to Find the Median of a Set of Numbers
Here is a complete worked example for a journalist reporting on household incomes (in USD):
Survey data: $32,000 · $45,000 · $52,000 · $47,000 · $38,000 · $210,000 · $49,000
- Sorted: $32,000 · $38,000 · $45,000 · $47,000 · $49,000 · $52,000 · $210,000
- n = 7 (odd), median position = 4
- Median = $47,000
- Mean = $67,571 — inflated by the $210,000 outlier
In this case, the median ($47,000) is far more representative of the typical household income than the mean ($67,571).
Frequently Asked Questions
What is the median in statistics?
The median is the central value in an ordered dataset. For n values sorted from smallest to largest, the median is the value at position (n+1)/2 for an odd count, or the average of positions n/2 and n/2+1 for an even count.
Why use the median instead of the mean?
Use the median when your data contains outliers or is heavily skewed. Classic examples include income distribution, house prices, response times, and medical test values where extreme cases can distort the mean significantly.
Can the median be used with Imperial and Metric measurements?
Yes. This calculator supports both US Imperial units (inches, feet, yards, miles, ounces, pounds, fluid ounces, gallons, etc.) and Metric (SI) units (mm, cm, m, km, mg, g, kg, mL, L, and temperature in °C and °F). Enter your measurements directly — the median formula works the same regardless of unit.
Can I calculate the median of currency values?
Yes. Select the Currency option and choose from 25 world currencies including USD, EUR, GBP, JPY, RUB, INR, BRL, CAD, AUD, and more. The median is displayed with the appropriate currency symbol.
What is the median of an even number of values?
When the dataset has an even number of values, there is no single middle number. The median is calculated as the arithmetic mean (average) of the two middle values. For example, for the dataset {3, 7, 8, 12}, the median is (7 + 8) / 2 = 7.5.
What if all values are the same?
If all values are identical, the median equals that value. For example, the median of {5, 5, 5, 5} is 5.
Is the median always one of the values in the dataset?
Not necessarily. For an odd number of values, the median is always a value from the dataset. For an even number of values, the median is the average of the two middle values, which may or may not itself appear in the original dataset.