Median Calculator

This Median Calculator helps you find the median of a list of numbers and shows each step clearly. It works by arranging the values in order and then identifying the middle value, or the average of the two middle values when there is an even number of data points. This makes it useful for checking answers, understanding how the median is calculated, and practising statistics step by step.

Step-by-step method

1. List the numbers and count how many there are.
2. Sort the numbers from smallest to largest.
3. Find the middle position (odd) or the two middle positions (even).
4. If odd, the median is the value in the middle position.
5. If even, add the two middle values and divide by 2.

Example 1: 1, 2, 3, 4, 5

Step 1 - List the numbers and count how many there are.

In this problem: The numbers are 1, 2, 3, 4, 5, so the count is n = 5.

Step 2 - Sort the numbers from smallest to largest.

In this problem: Sort the list: 1, 2, 3, 4, 5.

Step 3 - Find the middle position (odd) or the two middle positions (even).

In this problem: Because n = 5 is odd, the middle position is (5 + 1) ÷ 2 = 3.

Step 4 - If odd, the median is the value in the middle position.

In this problem: The 3rd value in the sorted list is 3, so the median is 3.

Final answer: Median = 3

Example 2: 1, 2, 3, 4

Step 1 - List the numbers and count how many there are.

In this problem: The numbers are 1, 2, 3, 4, so the count is n = 4.

Step 2 - Sort the numbers from smallest to largest.

In this problem: Sort the list: 1, 2, 3, 4.

Step 3 - Find the middle position (odd) or the two middle positions (even).

In this problem: Because n = 4 is even, the two middle positions are 2 and 3.

Step 4 - If odd, the median is the value in the middle position.

In this problem: The middle values are 2 and 3, so we add them: 2 + 3 = 5.

Step 5 - If even, add the two middle values and divide by 2.

In this problem: Now divide by 2: 5 ÷ 2 = 2.5.

Final answer: Median = 2.5