Average Calculator

Published on: July 20, 2025
Final Answer: Free • Full Steps: Plus

This Average Calculator finds the average of a list of numbers and shows the working line by line. The list is counted, the values are added into one total, and that total is divided by the count so it is shared equally between them. This is the same calculation as the mean, under the name most people use day to day. Following the same pattern every time is what makes the average easy to check and repeat for any list.

Step-by-step method

  1. Set up the problem.
  2. Count the values.
  3. Add the values together.
  4. Write the formula.
  5. Substitute the total and the count into the formula.
  6. Divide to get the average.

Formula:

\(\text{Average} = \frac{\Sigma x}{n}\)
See Example 1 Hide Example 1

Problem

\(5,\; 8,\; 12,\; 15\)

Approach

Step-by-step method

  1. Set up the problem.
  2. Count the values.
  3. Add the values together.
  4. Write the formula.
  5. Substitute the total and the count into the formula.
  6. Divide to get the average.

Step 1

Step 1 - Set up the problem.

In this problem: We are finding the average of the values \(5,\; 8,\; 12,\; 15\).

\(5,\; 8,\; 12,\; 15\)

Step 2

Step 2 - Count the values.

In this problem: Counting along the list reaches \(4\) at the last value, so \(n = 4\).

\(n = 4\)

Step 3

Step 3 - Add the values together.

In this problem: Adding the values in order gives \(5 + 8 + 12 + 15 = 40\).

\(\Sigma x = 5 + 8 + 12 + 15 = 40\)

Step 4

Step 4 - Write the formula.

In this problem: The average shares the total equally between the values, so the total is divided by how many there are.

\(\text{Average} = \frac{\Sigma x}{n}\)

Step 5

Step 5 - Substitute the total and the count into the formula.

In this problem: Replacing \(\Sigma x\) with \(40\) and \(n\) with \(4\) gives \(\text{Average} = \frac{40}{4}\).

\(\text{Average} = \frac{40}{4}\)

Step 6

Step 6 - Divide to get the average.

In this problem: Dividing the total by the count gives \(40 \div 4 = 10\).

\(\text{Average} = \frac{40}{4} = 10\)

Final Answer

\(\text{Average} = 10\)
See Example 2 Hide Example 2

Problem

\(6,\; 6,\; 7,\; 10\)

Approach

Step-by-step method

  1. Set up the problem.
  2. Count the values.
  3. Add the values together.
  4. Write the formula.
  5. Substitute the total and the count into the formula.
  6. Divide to get the average.

Step 1

Step 1 - Set up the problem.

In this problem: We are finding the average of the values \(6,\; 6,\; 7,\; 10\).

\(6,\; 6,\; 7,\; 10\)

Step 2

Step 2 - Count the values.

In this problem: Counting along the list reaches \(4\) at the last value, so \(n = 4\).

\(n = 4\)

Step 3

Step 3 - Add the values together.

In this problem: Adding the values in order gives \(6 + 6 + 7 + 10 = 29\).

\(\Sigma x = 6 + 6 + 7 + 10 = 29\)

Step 4

Step 4 - Write the formula.

In this problem: The average shares the total equally between the values, so the total is divided by how many there are.

\(\text{Average} = \frac{\Sigma x}{n}\)

Step 5

Step 5 - Substitute the total and the count into the formula.

In this problem: Replacing \(\Sigma x\) with \(29\) and \(n\) with \(4\) gives \(\text{Average} = \frac{29}{4}\).

\(\text{Average} = \frac{29}{4}\)

Step 6

Step 6 - Divide to get the average.

In this problem: Dividing the total by the count gives \(29 \div 4 = 7.25\).

\(\text{Average} = \frac{29}{4} = 7.25\)

Final Answer

\(\text{Average} = 7.25\)

Example Problems

Click one to load it into the box and solve it.