How to teach mean, median, mode and range
Year 7 (ages 12 to 13)
Mean, median, mode and range are four different ways to summarise a numerical data set: the mean is the equal-share average, the median is the sorted middle, the mode is the most frequent value, and the range is the spread from lowest to highest.
How to teach it
- Start with the mean as 'sharing the total equally': add every value, divide by the count.
- Teach the median as 'the sorted middle': sort the data first, then find the middle value (or average the two middle values for an even count).
- Introduce the mode as simply the most frequent value, and show it can be none, one, or several.
- Teach the range as highest minus lowest, a measure of spread rather than a typical value.
- Finish by comparing all four on one data set with an outlier, so students see why the 'right' average depends on the question.
Worked example
Data set: 2, 4, 4, 6, 9 Mean: (2+4+4+6+9) / 5 = 25 / 5 = 5 Median: sorted is 2, 4, 4, 6, 9, the middle (3rd) value is 4 Mode: 4 appears twice, more than any other value Range: 9 - 2 = 7
Common mistakes
- Assuming 'average' always means the mean, when it could mean any of the three.
- Finding the median without sorting the data first.
- Assuming every data set has exactly one mode.
- Confusing the range (a single number, the spread) with the number of values in the set.
Frequently asked questions
What is the difference between mean, median and mode?
The mean is the total of all values divided by how many there are, the median is the middle value once the data is sorted, and the mode is the value that appears most often. Each answers a different question about the same data, so a data set can have three different 'averages'.
When should you use the median instead of the mean?
Use the median when a data set has an outlier, one value much higher or lower than the rest, because the mean is dragged toward the outlier while the median is not. Salary and house-price data almost always quote a median for this reason.
Can a data set have no mode, or more than one mode?
Yes. If every value appears the same number of times, there is no mode at all; if two or more values tie for most frequent, the data set has more than one mode. Only the mean and median are always guaranteed to exist and be unique.
What grade or year is mean, median, mode and range taught?
In the Australian Curriculum this is a Year 7 skill (AC9M7ST01). It builds on simpler F-6 data-handling work and is the foundation for Year 9-10 skills like boxplots and comparing distributions.
Practise with free worksheets
Printable worksheets with answer keys that are never wrong.