Median Calculator
Reviewed by CalcMulti Editorial Team·Last updated: ·← Statistics Hub
The median is the middle value of a sorted dataset. Unlike the mean, it is not affected by outliers — making it the preferred measure of central tendency for skewed distributions such as income, housing prices, and reaction times.
Enter your values below to instantly find the median. The calculator also shows Q1, Q3, and the interquartile range (IQR).
Formula
Odd n: Median = x[(n+1)/2] | Even n: Median = (x[n/2] + x[n/2+1]) / 2
- n
- number of values in the dataset
- x[k]
- the k-th value in the sorted (ascending) dataset
Why the Median Is Resistant to Outliers
The median only depends on the middle value(s) — not the magnitude of extreme values. This makes it the preferred measure of central tendency for skewed distributions.
| Dataset | Mean | Median | Best choice |
|---|---|---|---|
| Salaries: $40K, $42K, $44K, $46K, $800K | $194K | $44K | Median — outlier distorts mean |
| Test scores: 70, 72, 74, 76, 78 | 74 | 74 | Either — symmetric data |
| House prices in a city | Skewed high by mansions | Middle market value | Median for "typical" price |
| Response times: 1.1, 1.2, 1.3, 1.4, 9.8 sec | 2.96 sec | 1.3 sec | Median — latency spike outlier |
Step-by-Step Example
Dataset: { 8, 3, 11, 5, 7, 1, 9 }
- 1Sort ascending: 1, 3, 5, 7, 8, 9, 11
- 2Count values: n = 7 (odd)
- 3Find middle position: (7 + 1) / 2 = position 4
- 4Read the value: 4th value in sorted list = 7
Even dataset example — { 4, 8, 12, 16 }: middle positions are 2 and 3 → values 8 and 12 → median = (8 + 12) / 2 = 10
Mean vs Median — Which to Report?
| Scenario | Mean | Median | Use |
|---|---|---|---|
| Salaries: $40K, $45K, $50K, $55K, $500K | $138K | $50K | Median — outlier skews mean |
| Exam scores: 70, 72, 74, 76, 78 | 74 | 74 | Either — symmetric, no outliers |
| House prices in a city | Pulled high by mansions | Middle market | Median for "typical" price |
| Lab measurements (normal distribution) | Best estimate | Similar to mean | Mean — uses all info |
Common Mistakes with the Median
Forgetting to sort first
The median requires sorted data. Finding the middle of unsorted values gives a random result, not the median.
Wrong middle index for even n
For even datasets, the median is the average of the two middle values — not the lower or upper one alone.
Confusing median with Q2
They are the same value — the median equals the 50th percentile (Q2). But Q1 and Q3 require a different calculation.
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Disclaimer
This calculator is for educational purposes only and does not constitute professional advice. Results are based on standard mathematical formulas. Always verify critical calculations with a qualified professional before making important decisions.