Mean, median and mode
Three ways to summarize a pile of data in one number
What is this about?
When you have lots of data (class grades, season goals...), you need one number that summarizes them. The mean shares the total equally, the median is the middle value once you sort the data, and the mode is the most repeated one. Each tells a different story about the same data.
The rule to remember
Mean: add everything and divide by how many data points there are. Median: sort the data from smallest to largest and take the middle one (if there are two middle values, average them). Mode: the most frequent value. Sorting BEFORE finding the median is mandatory.
Example 1
Mean of the grades 6, 8, 5, 9, 7
- 1Add all the data: 6 + 8 + 5 + 9 + 7 = 35.
- 2Count how many data points there are: 5 grades.
- 3Divide the sum by the count: 35 ÷ 5 = 7.
- 4The mean is 7: as if all 5 grades were a 7.
Result: 7
Example 2
Median of 3, 9, 4, 7, 12
- 1Sort from smallest to largest: 3, 4, 7, 9, 12.
- 2Count the data points: 5, so the middle one is the third.
- 3The third value is 7.
- 4The median is 7: as many values below it as above it.
Result: 7
Practice exercises
Solve them in your notebook, then check the solution.
1. Calculate the mean of: 10, 21, 14, 11
Show the solution
14
Mean = sum of values / number of values = (10 + 21 + 14 + 11) / 4 = 56 / 4 = 14
2. Calculate the range of: 14, 40, 13, 14, 32
Show the solution
27
Range = highest value - lowest value = 40 - 13 = 27
3. Find the mode of: 3, 8, 6, 3, 14, 3
Show the solution
3
The mode is the value that appears most often. 3 appears 3 times, more than any other number.
4. Calculate the range of: 10, 45, 3, 42, 47
Show the solution
44
Range = highest value - lowest value = 47 - 3 = 44
5. Find the mode of: 10, 4, 7, 4, 4, 11
Show the solution
4
The mode is the value that appears most often. 4 appears 3 times, more than any other number.
The most common mistake
Many people write
Median of 8, 2, 6 → the middle one is 2
Why it's wrong
The middle value was taken WITHOUT sorting first. Sort first: 2, 6, 8. The middle one is 6, not 2. The median only makes sense with sorted data.
Did it click?
The best way to find out is to try. These exercises are exactly on this topic.
Practise this topic