Mean Notes

Published on: September 29, 2026

This Mean Calculator finds the mean of a list of numbers and shows the working line by line. The mean shares the total equally between the values, so the list is counted, the values are added into one total, and that total is divided by the count. A value far from the rest pulls the mean towards it, which is worth knowing before trusting it. Following the same pattern every time is what makes the mean 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 mean.

Formula:

\(\bar{x} = \frac{\Sigma x}{n}\)
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 mean.

Step 1

Step 1 - Set up the problem.

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

\(\bar{x} = \frac{\Sigma x}{n}\)

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 \(\bar{x} = \frac{40}{4}\).

\(\bar{x} = \frac{40}{4}\)

Step 6

Step 6 - Divide to get the mean.

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

\(\bar{x} = \frac{40}{4} = 10\)

Final Answer

\(\bar{x} = 10\)
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 mean.

Step 1

Step 1 - Set up the problem.

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

\(\bar{x} = \frac{\Sigma x}{n}\)

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 \(\bar{x} = \frac{29}{4}\).

\(\bar{x} = \frac{29}{4}\)

Step 6

Step 6 - Divide to get the mean.

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

\(\bar{x} = \frac{29}{4} = 7.25\)

Final Answer

\(\bar{x} = 7.25\)
See Example 3 Hide Example 3

Problem

\(4,\; 9,\; 11,\; 16\)

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 mean.

Step 1

Step 1 - Set up the problem.

In this problem: We are finding the mean of the values \(4,\; 9,\; 11,\; 16\).

\(4,\; 9,\; 11,\; 16\)

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 \(4 + 9 + 11 + 16 = 40\).

\(\Sigma x = 4 + 9 + 11 + 16 = 40\)

Step 4

Step 4 - Write the formula.

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

\(\bar{x} = \frac{\Sigma x}{n}\)

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 \(\bar{x} = \frac{40}{4}\).

\(\bar{x} = \frac{40}{4}\)

Step 6

Step 6 - Divide to get the mean.

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

\(\bar{x} = \frac{40}{4} = 10\)

Final Answer

\(\bar{x} = 10\)
See Example 4 Hide Example 4

Problem

\(3,\; 5,\; 5,\; 7,\; 10\)

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 mean.

Step 1

Step 1 - Set up the problem.

In this problem: We are finding the mean of the values \(3,\; 5,\; 5,\; 7,\; 10\).

\(3,\; 5,\; 5,\; 7,\; 10\)

Step 2

Step 2 - Count the values.

In this problem: Counting along the list reaches \(5\) at the last value, so \(n = 5\).

\(n = 5\)

Step 3

Step 3 - Add the values together.

In this problem: Adding the values in order gives \(3 + 5 + 5 + 7 + 10 = 30\).

\(\Sigma x = 3 + 5 + 5 + 7 + 10 = 30\)

Step 4

Step 4 - Write the formula.

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

\(\bar{x} = \frac{\Sigma x}{n}\)

Step 5

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

In this problem: Replacing \(\Sigma x\) with \(30\) and \(n\) with \(5\) gives \(\bar{x} = \frac{30}{5}\).

\(\bar{x} = \frac{30}{5}\)

Step 6

Step 6 - Divide to get the mean.

In this problem: Dividing the total by the count gives \(30 \div 5 = 6\).

\(\bar{x} = \frac{30}{5} = 6\)

Final Answer

\(\bar{x} = 6\)