Mean Calculator

Published on: June 15, 2025
Final Answer: Free • Full Steps: Plus

This Mean Calculator helps you find the arithmetic mean of a list of numbers and shows each step clearly. It works by counting how many values there are, adding all the values together, and then dividing the total sum by the count. This makes it useful for checking answers, understanding how the mean 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 mean formula using the sum and the count.
  4. Substitute the values into the formula and simplify.

Formula:

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

Example 1: Take the set of numbers below.

\(1,\; 2,\; 3,\; 4,\; 5\)

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 \(n = 5\).

\(n = 5\)

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 \(\Sigma x = 15\).

\(\Sigma x = 1 + 2 + 3 + 4 + 5 = 15\)

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

In this problem: The mean is found by dividing the total sum \(\Sigma x\) by the number of values \(n\): \(\bar{x} = \frac{\Sigma x}{n}\).

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

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

In this problem: Substitute \(\Sigma x = 15\) and \(n = 5\): \(\bar{x} = \frac{15}{5} = 3\).

\(\bar{x} = \frac{15}{5} = 3\)

Final answer:

\(\bar{x} = 3\)

Example 2: Take the set of numbers below.

\(3,\; 10,\; 23,\; 12\)

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 \(n = 4\).

\(n = 4\)

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 \(\Sigma x = 48\).

\(\Sigma x = 3 + 10 + 23 + 12 = 48\)

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

In this problem: The mean is found by dividing the total sum \(\Sigma x\) by the number of values \(n\): \(\bar{x} = \frac{\Sigma x}{n}\).

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

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

In this problem: Substitute \(\Sigma x = 48\) and \(n = 4\): \(\bar{x} = \frac{48}{4} = 12\).

\(\bar{x} = \frac{48}{4} = 12\)

Final answer:

\(\bar{x} = 12\)