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?

Step-by-Step:

1

Add up the numbers.

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

Answer:

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.

See Also

What is a frequency table? Finding the mean from a frequency table Learn more about the mean ( interactive widget)