## The Lesson

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. ## Lesson Slides

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. ## Sum Over Count

The mean is the sum of the number divided by a count of the numbers.

## Outliers

Sometimes in a group of numbers, a few of them are much larger...
3, 5, 2, 7, 150
...or much smaller than the rest:
1, 502, 847, 564, 980
These relatively large (150) or small (1) numbers are called outliers. The mean is very affected by outliers, unlike the median. For example, consider the numbers:
1, 2, 3
The mean is 2 and the median is 2. If instead the numbers have a large outlier:
1, 2, 300
The mean is now 101 while the median is still 2. If you read about the average salary in a country, ask if it is the mean or median average? The mean average may dragged up by some very rich people, while the median won't be.

## How to Find the Mean from a Frequency Table

Sometimes data is presented in frequency tables. A frequency table representing the test scores is shown below: It is possible to find that the mean test score is 7.