Median Calculator

Find the median (the middle number calculator) by inputting your dataset below. You’ll get a detailed breakdown and analysis.

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Tip: Paste from spreadsheets, use commas, spaces, or newlines. Negative and decimal numbers work too.

Median (Middle Value)

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Central Tendency Measures

Median

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50th percentile

Mean

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Arithmetic average

Mode

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Most frequent

Distribution Shape:

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Left Skewed Symmetric Right Skewed

Data Distribution

Min Median Max

Five-Number Summary

Minimum

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Q1 (25th %ile)

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Median (Q2)

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Q3 (75th %ile)

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Maximum

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Median Position Details

Dataset Size

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Total values (n)

Median Position

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Method Used

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Spread & Variability

Range

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Max − Min

IQR

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Q3 − Q1

Std Deviation

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Sample (s)

Variance

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Sample (s²)

MAD (Mean)

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Mean Absolute Dev

MAD (Median)

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Median Absolute Dev

Coeff. of Variation

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CV = σ/μ × 100%

Related Median Measures

Trimean

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(Q1+2×Med+Q3)/4

Midhinge

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(Q1 + Q3) / 2

Midrange

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(Min + Max) / 2

Geometric Mean

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ⁿ√(x₁×x₂×...×xₙ)

Harmonic Mean

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n / Σ(1/xᵢ)

10% Trimmed Mean

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Excludes extremes

Winsorized Mean

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10% replaced

Key Percentiles

P5 —

P10 —

P20 —

P25 (Q1) —

P30 —

P40 —

P50 (Median) —

P60 —

P70 —

P75 (Q3) —

P80 —

P90 —

P95 —

P99 —

Dataset Overview

Count (n)

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Sum (Σx)

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Sum of Squares

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Unique Values

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Sorted Data (ascending)

Calculation Steps

Arrange data in ascending order

Count the number of values (n)

Determine if n is odd or even

Find the median value

When to Use Median vs Mean

✓ Use Median When

Data contains outliers or extreme values
Distribution is skewed (not symmetric)
Dealing with ordinal data
Reporting "typical" values (e.g., income, home prices)
Data has open-ended categories

✓ Use Mean When

Data is normally distributed (symmetric)
No significant outliers present
Further statistical calculations needed
All values are equally important
Working with ratio/interval data

The median is a robust measure of central tendency, less affected by outliers than the mean. It represents the exact middle of your sorted dataset.

What the Median Exactly Is?

The median is the middle value in a sorted dataset. Unlike the mean (average), which adds all values and divides by count, the median simply finds the center point where exactly half of your data falls above and half falls below. This makes it incredibly useful when dealing with skewed data or outliers that would otherwise distort your results.

How to Calculate Median

Finding the median requires just two steps: sort your data from smallest to largest, then locate the middle value. The process differs slightly depending on whether you have an odd or even count:

Odd count: The median is the exact middle number. For 7 values, it’s the 4th value.
Even count: The median is the average of the two middle numbers. For 8 values, average the 4th and 5th.

Median vs Mean: When to Use Each

Choosing between median and mean depends entirely on your data’s characteristics. The mean works well for symmetric distributions without extreme values, while the median excels when outliers are present or data is skewed.

Real-World Examples

Consider household income statistics. If nine households earn $50,000 and one earns $5,000,000, the mean income is $545,000—a number that represents nobody. The median remains $50,000, accurately reflecting the typical household. This is precisely why economists report median income rather than mean income.

Common Applications

Real estate: Median home prices prevent mansions from skewing market reports
Healthcare: Median survival times give patients realistic expectations
Education: Median test scores reveal true class performance

Properties of the Median

The median has several mathematical properties that make it valuable for statistical analysis. It minimizes the sum of absolute deviations from any central point, making it the optimal measure of center when using absolute distances. It’s also unaffected by extreme values—you could change the highest value to infinity and the median wouldn’t budge.

For perfectly symmetric distributions like the normal (bell) curve, the median equals the mean. When they differ, that gap reveals skewness in your data, helping you understand its underlying shape and choose appropriate analytical methods.