Step by step
The question
Question: find the third quartile, Q3, of 21, 24, 25, 28, 30, 33 and 35.
Q3 is the 75th percentile.
About 75% of the numbers are below it.
Q3 = the 75th percentile: about 75% are below it
They are already in order.
Small green numbers count the positions: 1, 2, 3, and so on.
1 Find the position
The position i: 75/100, times n plus 1.
n is how many numbers: 7.
i = 75100 × (n + 1)
75/100 is 0.75.
7 plus 1 is 8.
i = 0.75 × 8
0.75 times 8 is 6.
i = 6
Careful!
The rule uses n plus 1, not n.
That keeps the middle in the middle.
Careful: not 0.75 × 7 ✗
2 Count to the position
6 is a whole number.
We count to the 6th number: 33.
So the Q3 is 33.
Q3 = 33
3 Check
Let's check: 5 of the 7 numbers are below 33.
That is about 71%, close to 75%.
So it makes sense!
below 33: 5 of 7 = 71% ≈ 75%
Let's look back.
First: find the position.
Then: count to the position.
Last: check.
Answer
Q3 = 33