Median Calculator
Calculate dataset median (middle 50th percentile value), lower quartile Q1, upper quartile Q3, and Interquartile Range (IQR).
Calculate Dataset Median & Quartiles
Enter numbers separated by commas, spaces, or lines.
Calculation Results
Calculated by sorting array values in ascending order and selecting the middle observation position: \text{Median} = x_{(n+1)/2} \quad \text{for odd } n
Quick Summary
The Median Calculator evaluates the 50th percentile middle value of a sorted dataset, lower quartile Q1, upper quartile Q3, and Interquartile Range (IQR).
Formula Explanation
\text{Median for Odd } n: \text{Median} = x_{(n+1)/2}
\text{Median for Even } n: \text{Median} = \frac{x_{n/2} + x_{(n/2)+1}}{2}How It Works
The median represents the central 50th percentile of an ordered numerical sequence. The Median Calculator sorts your raw dataset in ascending order and computes the exact middle value for odd sample sizes $n$ or the average of the two central numbers for even $n$.
Step-by-Step Worked Example
Practical Problem: Calculate the median for the unsorted dataset: 14, 7, 22, 19, 31, 45, 11 ($n = 7$).
- Step 1: Sort dataset in ascending order:
7, 11, 14, 19, 22, 31, 45. - Step 2: Check sample size parity: $n = 7$ (Odd number of observations).
- Step 3: Determine middle position: Position $(7 + 1) / 2 = 4\text{th position}$.
- Step 4: Select 4th value from sorted list: The 4th number is $\mathbf{19.0000}$.
- Step 5: Interpretation: Exactly 50% of values are $\le 19$ and 50% are $\ge 19$.
Real-World Calculation Examples
Scenario 1: Odd Dataset Size (n = 7)
Parameters: 14, 7, 22, 19, 31, 45, 11
Result: Median 19.00 (4th element in sorted order).
Scenario 2: Even Dataset Size (n = 6)
Parameters: 10, 20, 30, 40, 50, 60
Result: Median 35.00 (Average of 30 & 40).
Scenario 3: Skewed Income Data
Parameters: $35k, $40k, $45k, $50k, $1,200k
Result: Median $45k (Robust against $1.2M outlier).
Scenario 4: Negative Temperature Readings
Parameters: -15, -10, -5, 0, 5
Result: Median -5.00 (Middle negative value).
Key Benefits of Using This Calculator
Outlier Resistant Measurement
Provides an accurate central tendency metric for highly skewed distributions.
Automatic Array Sorting
Sorts raw unordered datasets instantly into ascending numerical order.
Q1, Q3 & IQR Metrics
Computes 25th percentile Q1, 75th percentile Q3, and Interquartile Range (IQR).
100% Free & Client-Side
Executes locally in your browser with zero latency or web server transmission.
Frequently Asked Questions (FAQ)
What is median in statistics?
The median is the middle value separating the higher half from the lower half of a data sample.
Why is median preferred for skewed data?
Median is unaffected by extreme outliers, providing a realistic estimate of typical central values.
How is median calculated for an even number of values?
Average the two middle numbers in the sorted list ($\text{Median} = \frac{x_{n/2} + x_{(n/2)+1}}{2}$).
What percentile does the median represent?
The median represents the 50th percentile (Q2) of a cumulative frequency distribution.
What is Interquartile Range (IQR)?
IQR is the difference between the 75th percentile (Q3) and 25th percentile (Q1) ($\text{IQR} = Q3 - Q1$).
What is 1.5 × IQR rule for outliers?
Data points below $Q1 - 1.5 \times \text{IQR}$ or above $Q3 + 1.5 \times \text{IQR}$ are classified as statistical outliers.
Can median be equal to mean and mode?
Yes — in a perfectly symmetrical normal bell curve distribution, Mean = Median = Mode.
Can median be a decimal number when all inputs are integers?
Yes — if $n$ is even and the two middle integers differ (e.g. 10 and 11), the median is $10.5$.
How is median displayed in a boxplot (box-and-whisker plot)?
In a boxplot, the median is represented by the solid vertical line inside the central box.
What is median absolute deviation (MAD)?
MAD is the median of absolute deviations from the dataset median ($\text{MAD} = \text{Median}(|x_i - \text{Median}|)$).