Median Calculator
Find the median of any dataset instantly, with quartiles (Q1, Q3), IQR, five-number summary, interactive box plot, outlier detection using Tukey fences, percentile table, MAD, and Pearson skewness. Robust central tendency analysis for statistics, data science, and research.
10 values Β· even count β average of two middle values
βΆSorted values (10)
Median value
What Is the Median?
The median is the middle value of a dataset when sorted in order. It is the most widely used robust measure of central tendency because, unlike the arithmetic mean, it is not distorted by extreme values or outliers. Exactly 50% of values fall at or below the median β making it equivalent to the 50th percentile.
How to Use This Calculator
- 1Enter your dataPaste or type numbers separated by commas, spaces, or newlines. Or click a sample dataset to load example values instantly.
- 2Read the medianThe large result card shows the median and explains whether it is the exact middle value (odd count) or the average of two middle values (even count).
- 3Review the box plotThe interactive box plot visualises the five-number summary: min, Q1, median, Q3, max. Outlier dots appear in orange beyond the Tukey fences.
- 4Check IQR and outliersThe Spread & Distribution panel shows IQR, range, standard deviation, MAD, fence thresholds, and any detected outliers.
- 5Explore percentilesToggle Custom Percentiles to enter any percentile you need (e.g. P10 and P90 for decile analysis). The default table shows P10, P25, P50, P75, P90.
How the Calculations Work
Median
Always sort first. For odd n take index βn/2β. For even n average positions n/2 and n/2+1 (1-indexed).
Quartiles (Q1 & Q3)
Uses the inclusive interpolation method (same as Excel PERCENTILE.INC): value = sorted[i] + frac Γ (sorted[i+1]βsorted[i]) where i = (p/100)Γ(nβ1).
IQR & Tukey Fences
Values outside Q1 β 1.5ΓIQR or Q3 + 1.5ΓIQR are mild outliers. Beyond 3ΓIQR are extreme outliers.
MAD (Median Absolute Deviation)
Compute each value's absolute distance from the median, then take the median of those distances. Highly robust to outliers.
Skewness (Pearson's 2nd)
A quick non-parametric skewness estimate. Near 0 = symmetric; positive = right-skewed; negative = left-skewed.
Percentiles
where i = β(p/100)Γ(nβ1)β and frac = fractional part. This is the standard linear interpolation used by numpy, R, and Excel.
Worked Examples
β Odd Count β Test Scores
Dataset: 65, 69, 72, 76, 78, 83, 84, 88, 90, 91 (already sorted above β 10 values)
Wait β this is even. Let's use 7 values: 3, 7, 1, 15, 9, 4, 12
β‘ Even Count β Test Scores
Dataset: 65, 69, 72, 76, 78, 83, 84, 88, 90, 91 (10 values)
β’ Outlier Detection β House Prices (Β£000s)
Dataset: 290, 298, 300, 305, 315, 320, 325, 335, 410, 1250
β£ Skewness β Income Data
When median income is $45,000 but mean income is $72,000, the distribution is right-skewed (a small number of high earners pulls the mean up).
Frequently Asked Questions
Related Tools
Related Tools
Random Number Generator
Generate random numbers using three statistical distributions β Integer (discrete uniform), Float (continuous uniform), and Normal (Gaussian bell curve). Supports seeded output for reproducibility, no-duplicates mode, sort order, and instant statistics including mean, median, standard deviation, and mode.
Mean Calculator
Calculate all six types of mean simultaneously β Arithmetic, Geometric, Harmonic, Quadratic (RMS), Weighted, and Trimmed. Paste any dataset and instantly get the right average for your context, plus median, mode, standard deviation, variance, and coefficient of variation.
Mode Calculator
Find the mode(s) of any dataset with a complete frequency distribution table, visual bar chart, and automatic distribution type classification β unimodal, bimodal, multimodal, or amodal. Ideal for statistics, data science, surveys, and educational analysis.