The mean is one way to describe the center of data. The median and the mode are two others, and you find them by looking at a dot plot or an ordered list.
Key idea
The median is the middle value when the data are in order. With an even number of values, it is the mean of the two middle values. The mode is the value that appears most often.
Why it works
The median splits the data into two halves with the same number of values on each side. Only the order matters, not how far away the values are, so one very large or very small value hardly moves it. That is what makes the median a sturdy description of "the middle".
Worked example: Odd number of values
Find the median of 7, 2, 9, 4 and 5.
- Put them in order: 2, 4, 5, 7, 9.
- Five values, so the middle one is the 3rd: 5.
Answer: 5
Worked example: Even number of values
Find the median of 3, 8, 6, 10, 1 and 12.
- In order: 1, 3, 6, 8, 10, 12.
- Six values: the middle two are 6 and 8.
- Their mean is $(6 + 8) \div 2 = 7$.
Answer: 7
Worked example: The mode
Find the mode of 4, 7, 4, 9, 7, 4, 2.
- Count each value: 4 appears 3 times, 7 twice, 9 and 2 once.
Answer: 4
Common mistake
Taking the middle of the list as it is given, without putting it in order. For 7, 2, 9, 4, 5 the middle of the unordered list is 9, which is the largest value, not the middle one. Quick check: the median should have as many values below it as above it.