How to teach mean, median and mode
Grade 4 to Grade 6
An average is a single number that stands in for a whole set of data. There are three kinds. The mean is the total shared out equally (add them all, then divide by how many). The median is the middle value once the data is in order. The mode is the value that appears most often. The word 'average' on its own usually means the mean.
How to teach it
- Teach the mean as fair sharing: pool everything, then split it equally. Add the values and divide by how many there are.
- Teach the median by putting the numbers in order first, then finding the middle one; with an even set, take the mean of the middle two.
- Teach the mode as the most frequent value, noting there can be more than one, or none at all.
- Use the same small data set for all three so students see they can give different numbers.
- Discuss which average suits the data: the mean is pulled by an extreme value, the median is not.
Worked example
Data: 3, 7, 7, 2, 6 mean: (3 + 7 + 7 + 2 + 6) / 5 = 25 / 5 = 5 median: order 2, 3, 6, 7, 7 -> middle is 6 mode: 7 appears most -> 7
Common mistakes
- Forgetting to put the numbers in order before finding the median.
- Dividing by the wrong count when finding the mean.
- Confusing the three, giving the mode when the mean is asked for.
- Letting one very large or small value distort the mean without noticing.
Frequently asked questions
What are the mean, median and mode?
They are three kinds of average. The mean is the total shared out equally: add the values and divide by how many. The median is the middle value once the data is in order. The mode is the value that appears most often. On its own, 'average' usually means the mean.
What age or grade are mean, median and mode taught?
Mean, median and mode are usually taught from Grade 4 to Grade 6. Students learn each measure, apply all three to the same small data set to see they can differ, and discuss which suits the data best.
How do you work out the mean?
Add up all the values, then divide by how many there are. For the data 3, 7, 7, 2 and 6, the total is 25 and there are five values, so the mean is 25 divided by 5, which is 5. It is fair sharing: pool everything, then split it equally.
Why do you have to put numbers in order to find the median?
Because the median is the middle value, and 'middle' only makes sense once the data is sorted. If you pick the middle of an unordered list you get the wrong value. Order the numbers first, then find the middle one; with an even set, take the mean of the middle two.
When should you use the median instead of the mean?
Use the median when the data has an extreme value that would distort the mean. The mean is pulled towards a very large or very small value, while the median, the middle number, is not. So for data with an outlier, the median often represents the set more fairly.
What does the word average usually mean?
On its own, 'average' usually means the mean, the total shared out equally. But median and mode are also averages, so in a statistics context it is worth checking which is intended. Each can give a different number for the same data set.
Why does my child confuse the three averages?
Because they are all called averages and use the same data, children often give the mode when the mean is asked for, or forget to order the numbers before finding the median. Working all three out from one small data set, and labelling each, makes the differences clear.
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