Mean
The arithmetic average.
Key idea
The arithmetic average.
In depth
The mean is the sum divided by the count: it is the balancing point of the data. It uses every value, so it is sensitive to outliers and best for roughly symmetric data.
Worked example
Data 4, 8, 9, 11, 13: sum 45, n = 5, mean 9.
Formula
Real-world uses
- Calculating average monthly spending, average test score or average rainfall
Common mistake
Using the mean for strongly skewed data like incomes, where it misleads.
How to learn this
- Read the key idea and say it in your own words.
- Work through the worked example, then try a similar problem.
- Use the interactive lesson’s visual and mini-quiz to check the pattern.
Frequently asked questions
What is Mean?
The arithmetic average. It is a topic at the intermediate level in Probability & Statistics.
What is the formula for Mean?
The key formula is x̄ = Σx/n.
Where is Mean used in real life?
Real-world examples: Calculating average monthly spending, average test score or average rainfall.
What should I learn before Mean?
Make sure you are comfortable with Dot Plots and Stem-and-Leaf Plots, the previous topic in Probability & Statistics.
What is a common mistake with Mean?
Using the mean for strongly skewed data like incomes, where it misleads.
How can I practise Mean?
Open the interactive lesson, play with the visual, then answer the three-question mini-quiz. Getting two right marks the topic complete.
What comes after Mean?
Move on to Median next.
Related intermediate topics in Probability & Statistics
- Collecting Data and Sampling – Surveys, experiments and random sampling.
- Bias in Sampling – Systematic errors that make samples unrepresentative.
- Histograms – Bars showing frequency of numerical intervals.
- Dot Plots and Stem-and-Leaf Plots – Show the shape of small datasets.
- Median – The middle value of an ordered list.
- Range – Difference between maximum and minimum.