Median Calculator

This Median Calculator helps you find the median of a list of numbers and shows each step clearly. It works by counting the values, arranging them from smallest to largest, and then finding the middle value. If there is an even number of values, it finds the average of the two middle values instead. This makes it useful for checking answers, understanding how the median is calculated, and practising statistics step by step.

Step-by-step method

1. Count how many values are in the list. This gives the value of n.
2. Sort the values from smallest to largest.
3. Use n to decide whether there is one middle value or two middle values.
4. Find the middle value if n is odd, or average the two middle values if n is even.

Example 1: Take the set of numbers below.

Step 1 - Count how many values are in the list. This gives the value of n.

In this problem: The values are 1, 2, 3, 4, 5. There are 5 values, so n = 5.

Step 2 - Sort the values from smallest to largest.

In this problem: Ordering the values from smallest to largest gives 1, 2, 3, 4, 5.

Step 3 - Use n to decide whether there is one middle value or two middle values.

In this problem: Since n = 5 is odd, there is one middle position. The middle position is (5 + 1) ÷ 2 = 3.

Step 4 - Find the middle value if n is odd, or average the two middle values if n is even.

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

Final answer: The median is:

Example 2: Take the set of numbers below.

Step 1 - Count how many values are in the list. This gives the value of n.

In this problem: The values are 3, 10, 23, 12. There are 4 values, so n = 4.

Step 2 - Sort the values from smallest to largest.

In this problem: Ordering the values from smallest to largest gives 3, 10, 12, 23.

Step 3 - Use n to decide whether there is one middle value or two middle values.

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

Step 4 - Find the middle value if n is odd, or average the two middle values if n is even.

In this problem: The two middle values are 10 and 12. Average them: (10 + 12) ÷ 2 = 11.

Final answer: The median is: