1. Introduction: The Middle Value That Refuses to Be Fooled
Imagine your class has 5 students, and their marks in a test are 12, 15, 18, 20, and 95.
What is the "typical" mark here? If you compute the mean — add them all and divide by 5 — you get 160 / 5 = 32. But look at the data. Four out of five students scored 20 or less. Saying "the typical student scored 32" feels wrong, doesn't it? One unusually high score (95) dragged the mean up.
Here is another way to think about "typical". Line the marks up in increasing order: 12, 15, 18, 20, 95. Now point at the one standing exactly in the middle. That is 18. Half the students scored below 18, half scored above it. The 95 cannot drag it anywhere — even if that student had scored 950, the middle value would still be 18.
This middle value has a name: the median. The median is a measure of central tendency — a single number that represents the centre of the data — which gives the value of the middle-most observation.
Stop scrolling. Take the numbers 7, 3, 9, 1, 5. Arrange them in increasing order and find the middle one before reading on.
You should get 1, 3, 5, 7, 9 — and the middle value is 5. That is the median.
In this lesson you will first sharpen what you already know about the median from Class IX, and then learn the real skill of this chapter: finding the median when the data is grouped into class intervals and you cannot see the individual values at all.
You can now say in one line what a median is: the value of the middle-most observation when the data is arranged in order.