Median Calculator - Mathematical Calculations & Solutions
What is Median Calculator?
A median calculator is a statistical tool that finds the middle value in a dataset when the values are arranged in ascending or descending order. The median is a measure of central tendency that divides a dataset into two equal halves, making it particularly useful for understanding the typical value in skewed distributions.
The median calculation depends on whether the dataset has an odd or even number of values:
- Odd number of values: The median is the middle value after sorting
- Even number of values: The median is the average of the two middle values
- Formula for even count: Median = (n/2 value + (n/2 + 1) value) / 2
- Position for odd count: Median = (n + 1) / 2 position
How It Works
Input Data
Enter comma-separated numbers
Sort Values
Arrange in ascending order
Find Middle
Locate center value(s)
Median Calculation Rules:
- • Odd count (n): Median = value at position (n+1)/2
- • Even count (n): Median = (value at n/2 + value at n/2+1) / 2
- • Always sort first: Arrange values from smallest to largest
- • Robust statistic: Not affected by extreme outliers
Common Examples
House Prices ($000)
Test Scores
Ages (years)
Calculation Table
| Original Data | Sorted Data | Count | Middle Position(s) | Median |
|---|---|---|---|---|
| [3, 1, 2] | [1, 2, 3] | 3 (odd) | Position 2 | 2 |
| [4, 1, 3, 2] | [1, 2, 3, 4] | 4 (even) | Positions 2,3 | (2+3)/2 = 2.5 |
| [10, 20, 30, 40, 50] | [10, 20, 30, 40, 50] | 5 (odd) | Position 3 | 30 |
| [1, 100, 2, 99] | [1, 2, 99, 100] | 4 (even) | Positions 2,3 | (2+99)/2 = 50.5 |
| [42] | [42] | 1 (odd) | Position 1 | 42 |
Frequently Asked Questions
What is the median and how is it different from the mean?
The median is the middle value in a sorted dataset that divides the data into two equal halves. Unlike the mean (average), the median is not affected by extreme outliers, making it a more robust measure of central tendency for skewed distributions.
How do I calculate the median for even and odd number of values?
For odd count: The median is the middle value at position (n+1)/2. For even count: The median is the average of the two middle values at positions n/2 and (n/2)+1. Always sort the data first before finding the median.
When should I use median instead of mean or mode?
Use median for skewed distributions, when outliers are present, or for ordinal data. It's ideal for income data, house prices, and test scores where extreme values might distort the mean. Use mean for normal distributions and mode for categorical data.
Does the calculator automatically sort my data?
Yes, the calculator automatically sorts your input data in ascending order before calculating the median. You can enter numbers in any order, and the calculator will display both the original and sorted datasets for clarity.
What types of numbers can I use in the median calculator?
The calculator accepts all real numbers including positive integers, negative numbers, decimals, and fractions (entered as decimals). It automatically filters out invalid entries and works with any size dataset from a single value to hundreds of numbers.