Step by step
The question
Question: find the third quartile, Q3, of 41, 38, 45, 50, 36, 47, 52, 39, 44, 48, 55 and 42.
Q3 is the 75th percentile.
About 75% of the numbers are below it.
1 Put them in order
In order, smallest to biggest.
Small green numbers count the positions: 1, 2, 3, and so on.
2 Find the position
The position i: 75/100, times n plus 1.
n is how many numbers: 12.
75/100 is 0.75.
12 plus 1 is 13.
0.75 times 13 is 9.75.
Careful!
The rule uses n plus 1, not n.
That keeps the middle in the middle.
3 Count to the position
9.75 is not whole.
It is between the 9th and the 10th numbers: 48 and 50.
So we take the number halfway between them: add, then divide by 2.
48 plus 50 is 98.
Divided by 2: 49.
4 Check
Let's check: 9 of the 12 numbers are below 49.
That is about 75%, close to 75%.
So it makes sense!
Let's look back.
First: put them in order.
Then: find the position.
Then: count to the position.
Last: check.