Median Calculator Online
Find the median, mean, mode, quartiles Q1/Q3, IQR, and statistical outliers for any dataset.
Input Parameters
Live Result
Details
Steps
Step 1: Sort the data in ascending order: [12, 18, 24, 30, 42, 56, 70]
Step 2: Total number of observations (n) = 7
Since n = 7 is odd, the median is the single middle element at position (n + 1)/2 = 4: sorted[3] = 30
Step 4: Compute supporting quartiles: Q1 (25th percentile) = 18, Q3 (75th percentile) = 56, Interquartile Range (IQR) = 38
Quick Answer & Understanding Your Result
The Median is the middle value separating the higher half from the lower half of a sorted dataset: For an odd sample size n, Median = X_((n+1)/2); for an even sample size, Median = (X_(n/2) + X_(n/2+1)) / 2. Unlike the mean, the median is highly resistant to extreme skew and statistical outliers.
Five-Number Summary & Quartiles
- Minimum: The smallest observed data point in the ordered sample.
- First Quartile (Q1): The 25th percentile separating the bottom 25% of values.
- Median (Q2): The 50th percentile dividing the sample exactly in half.
- Third Quartile (Q3): The 75th percentile separating the top 25% of values.
- Maximum: The largest observed data point in the ordered sample.
Spread & Outlier Detection
- Interquartile Range (IQR): The statistical spread of the middle 50%: IQR = Q3 - Q1.
- Outlier Thresholds: Points lying outside [Q1 - 1.5×IQR, Q3 + 1.5×IQR].
- Robust Central Tendency: Median income or home prices accurately reflect population norms.
Paste or type your data values into the input field above to compute the median and full distribution summary instantly.
Formula & Calculation Logic
Mathematical FormulaAfter sorting the dataset in ascending order, the median is the exact center element (odd count) or arithmetic average of the two central numbers (even count).
Step-by-Step Guide
Enter Numbers
Paste or type values separated by commas, spaces, or line breaks.
Automatic Sort
The calculator filters non-numeric entries and sorts the array ascendingly.
Locate Center Element
Calculates the central index position depending on odd or even sample size.
Review Quartiles & Outliers
View median, quartiles Q1/Q3, IQR range, and detected statistical outliers.
Worked Examples Table
| Example | Input Values | Calculated Result | Explanation |
|---|---|---|---|
| Odd Dataset (7 values): 3, 13, 7, 5, 21, 23, 39 | Sorted: [3, 5, 7, 13, 21, 23, 39]. The 4th middle value is 13. | ||
| Even Dataset (8 values): 1, 2, 4, 7, 9, 12, 15, 18 | Sorted middle two values are 7 and 9. Median = (7 + 9) / 2 = 8. | ||
| Skewed Salary Dataset: 15, 18, 20, 22, 25, 28, 120 | The extreme outlier 120 raises the mean to 35.4, while median stays robust at 22. |
Frequently Asked Questions
Evidence-Based Methodology & Authoritative References
NIST/SEMATECH e-Handbook of Statistical Methods
Wolfram MathWorld - Statistical Median
Standard: ISO / W3C / IETF Authoritative Domain Standard
Formula: Odd n: Median = X_((n+1)/2)
Last Reviewed: August 21, 2026
Primary Source: NIST/SEMATECH e-Handbook of Statistical Methods
Reference Document: Wolfram MathWorld - Statistical Median
Computation Privacy: 100% client-side 0ms computation, zero data retention
Calculated results are modeled based on standard scientific and mathematical formulas. Please verify with domain-specific technical documentation for specialized applications.
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Calculated results are modeled based on standard scientific and mathematical formulas. Please verify with domain-specific technical documentation for specialized applications.