# How to Find the Mean

## Finding the Mean

We can find the mean of a set of numbers.

Imagine a teacher wanted to find the class's average test score in mathematics. ## How to Find the Mean

The mean is found by adding all the numbers together and dividing by how many numbers there are.

### Question

What is the mean of the test scores below? # 1

7 + 10 + 8 + 6 + 4 = 35

# 2

Divide the answer (35) by how many numbers there are. In our example, there are 5 students, so there are 5 test scores.

35 ÷ 5 = 7

The mean of the test scores is 7. ## Slider

The slider below gives another example of finding the mean.

Open the slider in a new tab

## A Formula to Find the Mean

The formula for finding the mean is shown below: In this formula,

• is the symbol for the mean. It is said "x bar".

• xi is each value, where i = 1, 2... n. n is how many numbers there are. In our example of the test scores:

x1 = 7, x2 = 10, x3 = 8, x4 = 6, x5 = 4

• Σxi means "sum of xi" from i = 1 (below the Σ) to n (above the Σ).

Σxi = x1 + x2 + ... + xn

In our example, n = 5

Σxi = x1 + x2 + x3 + x4 + x5

Σxi = 7 + 10 + 8 + 6 + 4

Σxi = 35

• This is all written above a line, with n under it. This means divide by n. In our example, n = 5:

x̄ = Σxi / n = 35 ÷ 5 = 7

The mean of the test scores is 7. What is a frequency table? Finding the mean from a frequency table Learn more about the mean ( interactive widget)