Median Calculator - Find the Middle Value of Any Data Set

The number that splits your data in half

Five houses sold for $180k, $210k, $225k, $240k, $1.2M. The average sale price is $411k. The median is $225k. Which number would you trust when deciding whether you can afford a house in this neighborhood? The median ignores extremes. The mean does not. Enter any set of numbers, and the calculator sorts them, finds the middle position, and explains the result.

Three steps, every time

Sort all numbers in ascending order. The calculator does this automatically.

Count. Odd number of values? Pick the middle one at position (n+1)/2. Even? Average the two middle values at positions n/2 and n/2+1.

Result. Exactly 50% of values sit below the median, 50% above. Outliers cannot move it.

Median vs mean - when each wins

Property	Median	Mean (average)
Outlier resistance	High	Low
Best for	Skewed data (income, prices)	Symmetric data (test scores)
Example: 1, 2, 3, 4, 100	3	22
Uses all values?	No (position only)	Yes
Reports that use it	Median income, house prices	Temperature, GPA

Practical examples

Home prices: $180k, $210k, $225k, $240k, $1.2M. Mean = $411k (misleading). Median = $225k (the actual middle of the market).
Real estate always reports median, not mean

Test scores: 55, 68, 72, 75, 78, 82, 91. Count = 7 (odd). Middle = 4th position. Median = 75. Mean = 74.43. Symmetric data: both are close.
For bell-shaped distributions, median approximates the mean

API latency: 12, 14, 15, 18, 22, 340 ms. Count = 6 (even). Median = (15 + 18) / 2 = 16.5 ms. Mean = 70.2 ms (distorted by 340 ms spike).
In tech, p50 (median) beats average latency for monitoring

Household income: $35k, $42k, $48k, $52k, $61k, $180k. Median = ($48k + $52k)/2 = $50k. Mean = $69.7k. The $180k earner inflates the mean by $20k.
Government statistics prefer median income for this exact reason

Single value: Data set: 42. Count = 1. Median = 42. With one element, median, mean, mode, and range are all the same.
A single value is its own median - always defined

FAQ

What is the difference between median and mean?

The mean sums all values and divides by the count. The median is the middle value after sorting. In {1, 2, 3, 4, 100}, mean = 22, median = 3. Use median when your data has outliers or is right-skewed (income, house prices).

How do you find the median of an even number of values?

Sort, then average the two middle values. For 6 values (a, b, c, d, e, f): median = (c + d) / 2. The result may not be one of the original values: {2, 4, 6, 8} gives median = 5.

Can the median be a decimal even if all inputs are integers?

Yes, when the count is even. {1, 3, 5, 7}: median = (3 + 5) / 2 = 4.0. {1, 2, 5, 8}: median = 3.5. Odd count: the median is always one of the original values.

Why do governments report median income?

Income is heavily right-skewed. A small number of very high earners pulls the mean upward. In a country where most earn $40-60k but some earn millions, mean = $75k, median = $52k. The median better represents the typical person.

What is p50 in software engineering?

p50 is the 50th percentile = the median. In API monitoring, p50 latency means 50% of requests are faster. Teams track p95/p99 for tail latency. If p50 = 15ms but p99 = 800ms, you have an outlier problem the median alone would miss.

How is the median related to quartiles?

The median is Q2 (second quartile). Q1 = median of the lower half. Q3 = median of the upper half. IQR = Q3 - Q1 measures spread without outlier influence. A value beyond Q1 - 1.5*IQR or Q3 + 1.5*IQR is flagged as an outlier.

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