BrainyCalculators
Login
Advertisement

M̃ Median Calculator

Find the median (middle value) of any data set. Also calculates Q1, Q3, interquartile range, and the five-number summary. Enter numbers separated by commas or spaces.

Median Formula

Odd count (n is odd)
Median = value at position (n + 1) / 2 after sorting
Even count (n is even)
Median = (value at n/2 + value at n/2 + 1) / 2
Interquartile Range
IQR = Q3 − Q1

How to Find the Median

  1. 1
    Enter Your Numbers
    Type numbers separated by commas or spaces. Order does not matter — the calculator sorts the data for you.
  2. 2
    Sort the Data
    Arrange all values from smallest to largest. The calculator does this automatically and shows the sorted list.
  3. 3
    Find the Middle Value
    For odd count, the median is the exact middle element. For even count, it is the average of the two middle elements.
  4. 4
    Read Quartiles and IQR
    Q1 is the median of the lower half, Q3 is the median of the upper half. IQR = Q3 − Q1 measures spread.

Worked Example

Data set: 1, 3, 3, 6, 7, 8, 9

Sorted: 1, 3, 3, 6, 7, 8, 9 (n = 7, odd)
Median = position 4 = 6
Lower half: 1, 3, 3 → Q1 = 3
Upper half: 7, 8, 9 → Q3 = 8
IQR = 8 − 3 = 5

Frequently Asked Questions

The median is the middle value of a data set when sorted in order. It divides the data into two equal halves. Unlike the mean, it is not affected by extreme outliers, making it a reliable measure of central tendency for skewed data.

When the count is even, there is no single middle value. Instead, take the average of the two middle values after sorting. For example, in {2, 4, 6, 8} the median is (4 + 6) / 2 = 5.

The IQR is the difference between Q3 (75th percentile) and Q1 (25th percentile). It represents the spread of the middle 50% of your data and is used to identify outliers. Values below Q1 − 1.5×IQR or above Q3 + 1.5×IQR are often considered outliers.

Use median when your data is skewed or contains outliers. For example, household income data is typically reported using the median because a small number of very high earners would inflate the arithmetic mean, making it unrepresentative of typical income.

Related Calculators

x̄ Statistics

Mean Calculator

Calculate arithmetic mean, geometric mean, and harmonic mean for any data set.

Calculate now
Mo Statistics

Mode Calculator

Find the mode (most frequent value) of any data set, including multimodal sets.

Calculate now
% Statistics

Percentile Calculator

Calculate percentile rank and find the value at any percentile in a data set.

Calculate now