Median Calculator
Calculate median, mean, and mode instantly. Enter your numbers and get results with step-by-step explanations.
Enter Your Numbers
Separate numbers with commas, spaces, or new lines
How to Use the Median Calculator
Step 1: Enter Your Numbers
Type or paste your set of numbers into the input field. Separate each number with a comma. You do not need to sort them first.
Step 2: Calculate
Click the Calculate button. The tool will instantly process your data and display the median value.
Step 3: View Results
Your median appears on screen. You also get the mean and mode for the same dataset. Copy the results to your clipboard with one click.
What is the Median in Statistics
The median is the middle value in a dataset when the numbers are arranged in order. It separates the higher half from the lower half of your data.
For an odd number of values, the median is the exact middle number. For an even number of values, the median is the average of the two middle numbers.
The median provides a better measure of central tendency than the mean when your data contains outliers or extreme values.
Median Calculation Examples
Example 1: Odd Number of Values
Dataset: 15, 8, 23, 4, 19
- Sort the numbers in ascending order: 4, 8, 15, 19, 23
- Find the middle position: (5 + 1) / 2 = 3
- Identify the median: The third number is 15
Median = 15
Example 2: Even Number of Values
Dataset: 12, 7, 18, 3, 25, 10
- Sort the numbers in ascending order: 3, 7, 10, 12, 18, 25
- Find the two middle positions: 3rd and 4th
- Calculate the average: (10 + 12) / 2 = 11
Median = 11
Example 3: Dataset with Outliers
Dataset: 5, 6, 7, 8, 100
Sorted: 5, 6, 7, 8, 100
Median = 7
Mean = (5 + 6 + 7 + 8 + 100) / 5 = 25.2
The median (7) better represents the typical value. The mean (25.2) is skewed by the outlier (100). This shows why the median is preferred for datasets with extreme values.
When to Use Median vs Mean
Use the median when:
- Your data contains outliers or extreme values
- You need a measure resistant to skewed distributions
- You work with ordinal data (rankings, ratings)
- You analyze income, housing prices, or test scores
Use the mean when:
- Your data is symmetrically distributed
- All values are equally important
- You need a measure sensitive to all data points
- You perform further statistical calculations
The median is the middle value. The mean is the arithmetic average. The median ignores extreme values. The mean includes all values in the calculation.
Mean and Median Calculator Features
This tool calculates both the mean and median at the same time. You enter your numbers once and get both measures of central tendency.
The mean adds all numbers and divides by the count. The median finds the middle value after sorting. Both measures help you understand your data distribution.
When the mean and median are close, your data is symmetrical. When they differ significantly, your data is skewed. This comparison reveals the shape of your distribution.
Mean Mode Median Calculator: All Three Metrics
This calculator provides mean, median, and mode in one tool. You get a complete statistical summary of your dataset.
- Mean: The arithmetic average of all values
- Median: The middle value when sorted
- Mode: The most frequently occurring value
These three measures work together to describe your data. The mean shows the balance point. The median shows the midpoint. The mode shows the most common value.
For example, in the dataset [2, 3, 3, 5, 7, 10]:
- Mean = (2 + 3 + 3 + 5 + 7 + 10) / 6 = 5
- Median = (3 + 5) / 2 = 4
- Mode = 3
Triangle Median Calculator: Geometric Median
The term median also appears in geometry. A triangle median is a line segment from a vertex to the midpoint of the opposite side.
Every triangle has three medians. These medians intersect at a single point called the centroid. The centroid divides each median in a 2:1 ratio.
To find a triangle median length, use this formula:
m = √(2b² + 2c² - a²) / 2
Where:
- m is the median length
- a is the side opposite to the vertex
- b and c are the other two sides
This is different from the statistical median. The statistical median finds the middle value in a dataset. The geometric median finds a line segment in a triangle.
Both concepts share the idea of finding a middle or central point. In statistics, you find the center of data. In geometry, you find the center of a triangle.
Median in Real-World Applications
Income Analysis
Median household income better represents typical earnings than mean income. High earners skew the mean upward. The median shows what a middle-class household earns.
Housing Prices
Median home prices reflect typical market values. A few luxury sales do not distort the median. Buyers and sellers use the median to understand real market conditions.
Test Scores
Median test scores show the middle performance level. A few perfect scores or failing grades do not shift the median. Teachers use the median to assess typical student understanding.
Salary Negotiations
Median salaries by job title guide fair compensation. The median shows what most people in a role earn. This helps both employers and job seekers set realistic expectations.
Health Metrics
Median blood pressure, cholesterol, or BMI values establish normal ranges. Outliers do not affect the median. Medical professionals use the median to define healthy population standards.
Frequently Asked Questions
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