Overview
An average is a value used to represent a set of numbers. The arithmetic mean is the most common type of average.
Objective
Calculate the mean and understand when median or mode may also be useful.
What You Need
- A list of values
- Calculator or paper
Before You Start
For the arithmetic mean, add all values and divide by the number of values.
How to Calculate
- Add all the values.
- Count how many values there are.
- Divide the total by the count.
- For the median, order the values and find the middle.
- For the mode, identify the most frequent value.
Worked Example
For 6, 8, 10 and 12: total = 36 and there are 4 values. 36 ÷ 4 = 9, so the mean is 9.
Useful Tips
- Write the count separately to avoid dividing by the wrong number.
- For money, round only at the end unless instructed otherwise.
- Use median when extreme values would distort the mean.
Common Mistakes
- Forgetting one of the values.
- Dividing by the wrong count.
- Assuming mean, median and mode are always the same.
Important Notes
Weighted averages give some values more influence than others and require multiplying each value by its weight before dividing by the total weight.
FAQ
What is the difference between mean and median?
The mean uses the total divided by the count; the median is the middle value after sorting.
Can there be more than one mode?
Yes, if multiple values occur equally often and more frequently than the others.