Median Calculator

The median calculator computes the median, mode, range, mean (average), count, and sum of a set of numbers.

Median:
Mean:
Mode:
Range:
Smallest:
Largest:
Count:
Sum:
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How to Use the Median Calculator?

  1. Firstly, enter or paste the data set in the input box.
  2. Make sure the data set should be space or comma separated. For example 1 5 7 8 10 4   or  1, 5, 7, 8, 10, 4.
  3. After entering the values, click the 'Calculate' button.
  4. As a result, the tool will show the median, mean (average), mode, range, smallest, largest, count, and sum results.
  5. For new calculations, click the 'Reset' button.

What is Median?

Median is a statistical concept that measures central tendency. In other words, it's a value that represents the center of the sorted observation. It gives the point from where 50% of data is more and 50% of data is less. It's widely used in statistical data analysis.

How to Calculate Median?

The median is calculated using the following formulas.

Median Formula for Odd Data Set

Median = X(n+1/2)

Where,
n = size of the data set.

Quick Tip: For the odd data set, the median value will be exactly in the middle of the data set.

Let's take an example.

Example:

Find the median for the data set: 4, 6, 2, 7, 1.

Solution:

Firstly, sort the numbers in ascending order: 1, 2, 4, 6, 7.

The size of the data set is odd. So, the middle number of the data set is the median.

So, median = 4.

Calculation:

Median = X(n+1/2)

= X(5+1/2) = X(6/2) = X3

After sorting, check the 3rd value of the data set: 1, 2, 4, 6, 7.

So, the Median = 4.

Median Formula for Even Data Set

Median = (X(n/2) + X(n/2 + 1)) / 2

Where,
n = number of values.

Quick Tip: If the data set is even, the median will be the mean or average of the two numbers that are in the middle of the data set.

Let's take an example.

Example:

Find the median for the data set: 3, 6, 1, 7, 8, 12, 4, 14.

Solution:

Firstly, sort the numbers into ascending order: 1, 3, 4, 6, 7, 8, 12, 14.

Here, the size of the set is even. Therefore, the mean or average of the two middle numbers is the median.

The two middle numbers are 6 and 7.

Mean = (6 + 7) / 2 = 13/2 = 6.5.

So, Median = 6.5.

Calculation:

Median = ( X(n/2) + X(n/2 + 1) ) / 2

= ( X(8/2) + X(8/2 + 1) ) / 2

= ( X(4) + X(5) ) / 2

Now, find the 4th and 5th values from the data set. That is 6 and 7.

= (6 + 7) / 2 = 13/2 = 6.5

So, the Median = 6.5.