The LessonWe 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 MeanThe mean is found by adding all the numbers together and dividing by how many numbers there are.
QuestionWhat is the mean of the test scores below?
Add up the numbers.
7 + 10 + 8 + 6 + 4 = 35
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.
Lesson SlidesThe slider below gives another example of finding the mean. Open the slider in a new tab
A Formula to Find the MeanThe formula for finding the mean is shown below:
In this formula,
- x̄ 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 + ... + xnIn our example, n = 5Σxi = 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
Sum Over CountThe mean is the sum of the number divided by a count of the numbers.
OutliersSometimes 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, 980These 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, 3The mean is 2 and the median is 2. If instead the numbers have a large outlier:
1, 2, 300The 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 TableSometimes 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.
Read more about finding the mean from a frequency table