Mode, median and range · Usually met around P5
The median
Sort first, then find the middle.
How to do it
Method
Sort first, then find the middle
4, 9, 2, 7, 5 → 2, 4, 5, 7, 9: median 5
Another way
Cross off both ends
Cross off 2 and 9, then 4 and 7 → 5
In full
The median is the middle value once the data are sorted from smallest to largest. Always sort first! With an odd number of values there is one in the middle: for 7 values the median is the (7 + 1) ÷ 2 = 4th. With an even number there are two in the middle, and the median is halfway between them: (12 + 15) ÷ 2 = 13.5, so the median need not be one of the data. Another way: once sorted, cross off the smallest and the largest, one each at a time; the one left (or halfway between the two left) is the median.
Worked examples
Have a go first, then open each one for the answer and the working.
Example 1
Data: 18, 1, 12, 9, 13, 4, 11. What is the median?
Show the answer and working
Answer: 11
Sort first: 1, 4, 9, 11, 12, 13, 18. With 7 values the middle is the 4th: 11.
Example 2
Data: 22, 37, 19, 34, 27, 19. What is the median?
Show the answer and working
Answer: 24.5
Sorted, 6 values have two in the middle, 22 and 27. Median = (22 + 27) ÷ 2 = 24.5.
Example 3
Data: 28, 15, 35, 21, 27. What is the median?
- A. 27
- B. 3
- C. 35
- D. 25
Choose the right answer
Show the answer and working
Answer: A. 27
Sort first: 15, 21, 27, 28, 35. The middle one is 27.
Practise it in the game →Mode, median and range · Free to start, unlimited questions, no download