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?
StepbyStep:
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.
A Formula to Find the Mean
The formula for finding the mean is shown below:
In this formula,

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

x_{i} is each value, where i = 1, 2... n. n is how many numbers there are. In our example of the test scores:
x_{1} = 7, x_{2} = 10, x_{3} = 8, x_{4} = 6, x_{5} = 4

Σx_{i} means "sum of x_{i}" from i = 1 (below the Σ) to n (above the Σ).
Σx_{i} = x_{1} + x_{2} + ... + x_{n}
In our example, n = 5
Σx_{i} = x_{1} + x_{2} + x_{3} + x_{4} + x_{5}
Σx_{i} = 7 + 10 + 8 + 6 + 4
Σx_{i} = 35

This is all written above a line, with n under it. This means divide by n. In our example, n = 5:
x̄ = Σx_{i} / n = 35 ÷ 5 = 7
The mean of the test scores is 7.