Average Calculator

This Average Calculator helps you find the average of a list of numbers and shows each step clearly. It works by counting how many values there are, adding the values together, and then dividing the total sum by the count. This makes it useful for checking answers, understanding how the average is calculated, and practising statistics step by step.

Step-by-step method

1. Count how many numbers are in the list. This gives the value of n.
2. Add all the numbers together to find the total sum, Σx.
3. Write the average formula using the sum and the count.
4. Substitute the values into the formula and simplify.

Formula:

Example 1: Take the set of numbers below.

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

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

Step 2 - Add all the numbers together to find the total sum, Σx.

In this problem: Add the numbers: 1 + 2 + 3 + 4 + 5 = 15. So the total sum is Σx = 15.

Step 3 - Write the average formula using the sum and the count.

In this problem: The average is found by dividing the total sum Σx by the number of values n.

Step 4 - Substitute the values into the formula and simplify.

In this problem: Substitute Σx = 15 and n = 5, then simplify to get 3.

Final answer: The average is:

Example 2: Take the set of numbers below.

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

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

Step 2 - Add all the numbers together to find the total sum, Σx.

In this problem: Add the numbers: 3 + 10 + 23 + 12 = 48. So the total sum is Σx = 48.

Step 3 - Write the average formula using the sum and the count.

In this problem: The average is found by dividing the total sum Σx by the number of values n.

Step 4 - Substitute the values into the formula and simplify.

In this problem: Substitute Σx = 48 and n = 4, then simplify to get 12.

Final answer: The average is: